One of these things is not like the others...

[Eomer of the Rohirrim]

A fine topic.

Don't you think that the notion of the 'authors' of the books was of secondary importance? The unexplained entities allow the reader to become even more involved in the fantasy. I think this was of primary importance to the storyteller. The quaint idea of inventing different authors was a lovely touch allowed for by the way Tolkien told—and concealed—the story and its elements.

[Raynor]

Which is why we are fixated upon and fascinated by the likes of Bombadil, the Stone Giants, the speaking thrush, Beorn, even Orcs/Goblins, Trolls and Dragons, Werewolves, Vampires and Wargs.

Some of them are, indeed, intended enigmas - such as Bombadil:

Originally Posted by Letter #144

And even in a mythical Age there must be some enigmas, as there always are. Tom Bombadil is one (intentionally).

Though I can't recall the letter at the moment, he did state that he wanted others to continue his cycle. The stone giants are a passing refference - but we do see pairs of good evil for almost everything - even Tulkas represents the good side of violence cf Myths Transformed, so maybe Melkor's (?) evil trolls have good counterparts - as in the Letters and in LotR, he rejects the idea of something completely evil. Concerning speaking animals, Tolkien did complain about it:

Originally Posted by Orcs, Myths Transformed, HoME X

What of talking beasts and birds with reasoning and speech? These have been rather lightly adopted from less 'serious' mythologies, but play a part which cannot now be excised. They are certainly 'exceptions' and not much used, but sufficiently to show they are a recognized feature of the world. All other creatures accept them as natural if not common.

The rest of the bunch are indeed interesting, Beorn, wargs, werewolves, etc, but I do think that their primary home, of all the possible humanly conceivable ones, is in fantasy. That is their right place, and they fit with the laws of the created universe, and therefore have a positive participation to the success of the story, not the other way around. However, I do believe that there were things that were beyond what he deem possible to correct:

Originally Posted by Letter #131

It is not possible even at great length to 'pot' The Lord of the Rings in a paragraph or two. .... It was begun in 1936 and every part has been written many times. Hardly a word in its 600,000 or more has been unconsidered. And the placing, size, style, and contribution to the whole of all the features, incidents, and chapters has been laboriously pondered. I do not say this in recommendation. It is, I feel, only too likely that I am deluded, lost in a web of vain imaginings of not much value to others — in spite of the fact that a few readers have found it good, on the whole. What I intend to say is this: I cannot substantially alter the thing. I have finished it, it is 'off my mind': the labour has been colossal; and it must stand or fall, practically as it is.

[doug*platypus]

Mithadan

He didn't have the time to fix his little "inconsistencies"? I don't buy that.

Ah, but I didn't commit myself fully there. I stated that he lacked either the time or the inclination to explain everything away. You make a good case for him having the time available, so that leaves only the inclination.

Raynor has once again provided the right quote at the right time:

Letter #131

What I intend to say is this: I cannot substantially alter the thing. I have finished it, it is 'off my mind': the labour has been colossal; and it must stand or fall, practically as it is.

This quote implies that there was some reluctance to revisit LOTR; this reluctance extending possibly even to the origins of some of the unexplained creatures contained within the book.

We know that Tolkien continued to work on his invented world after publication of LOTR. Why did he not choose to write complete back stories or creations for Bombadil, dragons and giants? Was it because he was too busy with the actual events of the First and Second Ages? Did the mystery elements of The Hobbit and LOTR get nudged aside, as the Professor was preoccupied? Or was it a conscious decision to leave the ambiguity as it was?

Bilbo made mistakes or misinterpretations of what he saw and experienced. A lightning storm becomes Stone Giants. Howling wargs seem to be speaking. Gandalf (perhaps) paralyzes Trolls and Bilbo attributes this to the effect of the sun.

In defence of the original Mr Baggins, and The Hobbit, Gandalf also believed in the Stone Giants, saying that he would have to find a more or less decent giant to stop up the cave in which the dwarves and Bilbo were captured. And in FOTR, Aragorn tells the hobbits that it would be impossible for a troll to be abroad in the sunlight. Surely the lore of Gandalf and Aragorn is to be trusted? I would say they are almost as authoritative as the narrator himself? Dog waiters we may have a bit more of a struggle to reason with!

[Boromir88]

Ah, but I didn't commit myself fully there. I stated that he lacked either the time or the inclination to explain everything away. You make a good case for him having the time available, so that leaves only the inclination.~Doug

I think you can even make a case for both. Probably earlier on in his life he had time to spend and work on everything. However, as he got older it seemed like he got rather bogged down with trying to 'answer' everything, saying that everybody wanted an answer for something. Also, as he got older his health began to decline. So, I think you can make a case for both. Here are a few related quotes:

... while many like you demand maps, others wish for geological indications rather than places; many want Elvish grammars, phonologies, and specimens; some want metrics and prosodies.... Musicians want tunes, and musical notation; archaeologists want ceramics and metallurgy; botanists want a more accurate description of the mallorn, of elanor, niphredil, alfirin, mallos, and symbelmynë, historians want more details about the social and political structure of Gondor; general enquirers want information about the Wainriders, the Harad, Dwarvish origins, the Dead Men, the Beornings, and the missing two wizards (out of five).~Letter to H. Cotton Minchin

I don't think he ever lost a love for his books, but I do sense that he did get bogged down (and even tired) with consistently trying to answer everyone's questions about it. Compile that upon with his declining health. Consistently through Letters he responds with being 'sorry' for answering so late but his health didn't permit it...here are just a few:

I am sorry for the long delay, I was unwell for some time, and then faced by a family laid low one by one by influenza.~Letter #9

I have been unwell since I last saw you – in fact I reached the edge of a breakdown, and was ordered by the doctor to stop short. I have done nothing for a week or two – being in fact quite unable.~Letter #33

I have worked under difficulties of all kinds, including ill-health.~Letter #35

These are all around the age of when Tolkien was in his fourties, and by much later his health gets dramatically worse:

I am (temporarily, I hope) deprived of the use of my right hand and arm….~Letter #245

I have been ill, and am still suffering from rheumatism in my right arm…~Letter #247

His publishers Rayner Unwin and George Allen also noticed the health of his wife may have contributed to part of the problem:

Even more distracting was the declining health of his wife….It was Edith’s ill-health that precipitated their move from Holywell to the ‘high dry soil’ of Headington in 1953, and later in 1968 to Bournemouth. But even there arthritis and other illnesses continued to afflict her. She was in hospital in 1958. Soon after coming out she broke her arm, and two years later she was back in hospital again~Allen & Unwin A Rememberence Chapter

With all that being said. I don't necessarily think that him not finishing things was completely due to a lack of time, or a lack of inclination. I do see what Mithadan is saying in that I think some things he left purposefully unanswered to put out in the public and see how the public viewed his books:

Practically speaking of course, none of the Matter of Middle-earth was ';finished'; but continued to evolve, and was open to second thoughts while Tolkien lived.~The Development of Tolkien's Legendarium

Of course the L.R. does not belong to me. It has been brought forth and must now go its appointed way in the world, though naturally I take a deep interest in its fortunes , as a person would of a child.~Letter #328

So, there definitely seems to be not just one specific defined answer, but several. Some things he wanted to purposefully leave unanswered (I think perhaps Tom Bombadil is the best example). Also, there were the problems of his health which contributed to a lack of time and a lack of inclination.

[Durelin]

I started on this response yesterday and finished it only today, so it might seem a little disjointed. Also, I started it before any of the major Letters and HoME (and the like) quotage, so it's all my speculation...and I'm going back to good ol' Tom.

Originally Posted by Mithadan

LoTR? Written by Frodo. More wordly and better educated. But still a Hobbit and subject to the flaws of a Hobbit's interpetation of matters beyond his experience.

And so Frodo's description of Tom Bombadil is from his experience, and can be nothing more. From the way he is described we can tell that Frodo had the utmost reverence for Tom, and was obviously mystified by him. So I suppose he would not bother even speculating who/what Tom was: likely he thought it unnecessary.

But is it just Frodo who thought it unnecessary, or did Tolkien see it as such, as well? I expect he probably did.

I think Tolkien really wanted to keep people from getting too settled into Middle-earth. He wanted it to be entertainingly fantastical, and not stop tugging at the strings of our imagination. First he gets us all settled in with this idea of Hobbits. Then he throws in things like Elves, 'moving trees,' a magical Ring, a Dark Lord... We start off 'being with' Hobbits, which are really rather familiar to us, and we learn about all these things that are far from really familiar to us through them. Next thing, we experience the first meeting of the Ringwraiths with Frodo. We experience Elves for the first time.

But with all of this dark stuff: the Ringwraiths, the Ring, a Dark Lord, a scary forest, one very nasty tree, and overall a very unfortunate situation for Frodo, there seems to be very little light. All of the power seems to be on the side of all the dark stuff, while on the side of light there are just a few Hobbits - even the Wizard is nowhere to be found. Tom Bombadil shows up at such a perfect moment, and shows us the power of good in Middle-earth just as blatantly as Sauron and the Ring show us the power of evil. Just when the Hobbits are pretty much literally swallowed up, by darkness you could say, this mysterious Tom enters.

[Raynor]

Here is the quote concerning the legacy Tolkien left for others to complete his work (well, he at least intended that initially):

Originally Posted by Letter #131

I would draw some of the great tales in fullness, and leave many only placed in the scheme, and sketched. The cycles should be linked to a majestic whole, and yet leave scope for other minds and hands, wielding paint and music and drama.

More wordly and better educated

Then again, Tolkien did note (and perhaps regret) the difference between his two works

Originally Posted by Letter #125

After all the understanding was that you would welcome a sequel to The Hobbit, and this work can not be regarded as such in any practical sense, or in the matter of atmosphere, tone, or audience addressed.

Originally Posted by Letter #131

The generally different tone and style of The Hobbit is due, in point of genesis, to it being taken by me as a matter from the great cycle susceptible of treatment as a 'fairy-story', for children. Some of the details of tone and treatment are, I now think, even on that basis, mistaken. But I should not wish to change much. For in effect this is a study of simple ordinary man, neither artistic nor noble and heroic (but not without the undeveloped seeds of these things) against a high setting — and in fact (as a critic has perceived) the tone and style change with the Hobbit's development, passing from fairy-tale to the noble and high and relapsing with the return.

But still a Hobbit and subject to the flaws of a Hobbit's interpetation of matters beyond his experience.

If I interpret the LotR Prologue correctly, LotR is actually an improved Thain's Book, (itself a copy after the Red Book kept at the Undertowers, the home of the Fairbairns, Wardens of the Westmarch, and it received "many corrections" in Gondor. These corrections probably eliminated the inconsistencies that appeared due to the peculiar skill (or lack thereof) of the hobbits in writting down the events. I would also note that in Letter #168 the following meaning of Frodo is given:

Frodo is a real name from the Germanic tradition. Its Old English form was Froda. Its obvious connexion is with the old word frod meaning etymologically 'wise by experience', but it had mythological connexions with legends of the Golden Age in the North.

Of Merry we know that he also received wisdom from his experience with evil:

Originally Posted by The houses of healing, RotK

But these evils can be amended, so strong and gay a spirit is in him. His grief he will not forget; but it will not darken his heart, it will teach him wisdom.

So, all in all, Frodo's more terrible experiences, the bearing of the ring, and the wound he received, helped him mature more quickly, and write a better work at an earlier age than Bilbo:

Originally Posted by Letter #153

Suffering and experience (and possibly the Ring itself) gave Frodo more insight; and you will read in Ch. I of Book VI the words to Sam.

So I suppose he would not bother even speculating who/what Tom was: likely he thought it unnecessary.

He did question Goldberry about who Tom is, although her answer, "he is", left many people wondering whether Tom is Eru, but Tolkien rejected this particular idea firmly:

Originally Posted by Letter #153

[Peter Hastings cited the description of Bombadil by Goldberry: 'He is.' Hastings said that this seemed to imply that Bombadil was God. ]
...
As for Tom Bombadil, I really do think you are being too serious, besides missing the point.

[Estelyn Telcontar]

In my opinion, Tolkien himself wanted the enigmas to stay enigmatic - even to and for himself! Do you think he had all of the background figured out and just chose to keep that information from his readers on purpose? Boro has a point with JRRT's inability to resolve some of the mysteries due to health problems later in life, but I propose that he did not want to cut the ball open so that it would not lose its bounce for him. Or, to speak with Gandalf:

...he that breaks a thing to find out what it is has left the path of wisdom.

I suggest that Tolkien wanted to keep at least a bit of Faery's mystery for himself.