"Weel done, Cutty-sark!" -Mithril, Moria and Valinorean ship-building
 

Bit of a random title I know but watching the poor Cutty Sark burn down didn't just remind me of the time in 1997 when I went hilariously missing for three hours and was eventually picked up by the police when my family and I went out to see the last tea-clipper when she visited Aberdeen.

Not a nice memory, but anyhow it, also a bit randomly having recently rearead Bilbo's song in Rivendell, made me wonder how they managed to build Earendil's boat out of Mithril in Valinor, when according to Gandalf, Moria was the only place in the world where Mithril was found. How did they find the rare metal? It seems unlikely that there was trade between Khazad-dum and Valinor and I doubt Earendil himself took enough to rebuild his ship. Was it artistic license on Bilbo's part?

Is Valinor included in the word "world", or does "the world" only mean the lands east of the Sea?

I doubt Aulë would have stored such a metal as mithril only in one place in Eä, so it's possible that it was found also in Valinor.

No, clearly it is implied in the world at that time.
We know that mithril was also found in Númenor:

Indeed, a strange thing, though I personally rather believe that Gandalf still said the truth, since Númenor was underwater and Aman had been taken away from the world.

Looking at Wikipedia, they mention that there are indications that Mithril was present in both Numenor and Aman in smaller quantities than in Moria. I wish that the reference would have been noted in the article, as I'm wondering if it was deduced by the building of a certain aforementioned ship.

Another interesting tidbit was that Moria might have been the only soure in the Third Age, which agrees nicely with The Might's thoughts.

Wikipedia's article on Mithril

If memory serves, there's a footnote somewhere in Unfinished Tales that provides the basis for the speculation about mithril being found in Valinor and Númenor.

However, I'd like to address the Might:

Actually...

In Tolkien's earlier writings, especially, "the world" quite often does NOT inclusively refer to Valinor. This was particularly the case in the The Book of Lost Tales, when the conception of the Straight Road and the the Round World after the Akallabêth had not yet been conceived. Tolkien several times refers to "the world" as "everywhere but Aman"--or what afterwards came to be named Aman.

I'm not sure how prevalent this usage of "the world" becomes after the Book of Lost Tales, but I think it would be unwise to write off the possibility of Aman having mithril simply on the basis of it having been "in the world".

Just a couple of points:
 

Also Gandalf was talking mainly to the hobbits and the world for them was effectively Middle Earth.

It's not said here that mithril was used to make the vessel "fair and marvellous".

I think that this may be the case. The verses in question are made up by Bilbo, rather than a translated story, so it's quite possible that he took some liberties in his description. Take the 2nd verse of Bilbo's poem for example,... is Earendil's helmet really made of adamant? Also Bilbo's statement that "a ship then new they built for him" is at odds with the description in the Silmarillion that what the Valar did do was to hallow Vingilot itself and set it in the heavens.

One wonders if Aragorn would have allowed Bilbo to take much artistic license. Remember his words, reported by Bilbo to Frodo later--about having "cheek" to write verses about Eärendil in the house of Elrond?

Which isn't to say that Bilbo didn't....

This statement suggested to me that Aragorn was content to let Bilbo be. It is after all a poem, not a historical treatise. If Bilbo wishes to describe Earendil's ship as being made of mithril, Aragorn might wonder briefly where Bilbo got that notion but wouldn't spend a lot of time arguing with him about it. I mean are mithril ships any more far fetched than say, elven warrior princesses?:)