[Boromir88]

MoS:

For example, Celeborn knew that the bridges at Osgiliath were cast down and the landings held by the Enemy.

Boromir gave his account at the Council, Celeborn states one of the few people he still remains in contact with is Elrond. Communication between Rivendell and Lorien makes sense.

Communication between Gondor and Rivendell and/or Lorien doesn't. First off, Rohan and Gondor have this major rumor that Lorien is run by a witch and should be avoided (even Faramir believes it.) Secondly, Boromir talks about Gondor's "loneliness" and seemingly the only remaining bastion against Sauron, besides their friends in Rohan. Boromir was being pretty arrogant, because of course other people were opposed to Sauron, but the fact that he states Gondor's only friends now are Rohan, to me suggests, Rohan is the only place Gondor would be in contact with.

You have to remember Denethor was prideful and distrusted anyone who did not fight for Gondor, he was in the mindset it is Gondor vs. Mordor, and isolated Gondor from the rest of its allies, including Rohan (see the Appendix: Stewards).

It's already been established that the location of Rivendell is not a common known thing, or else it would not have been a very effective refuge. I mean Gondor (nor the people of Middle-earth) did not have GPS to plot out their route. If Boromir even looked at a map before he left to get a general sense of direction, "a map" (if Rivendell was even on it!) would not be able to show him recognizable landmarks through woods, or show him how to find a hidden location, in a secret valley, in an area that was completely unfamiliar. Boromir was not a ranger, and the resident ranger even had trouble finding the way to Rivendell.

Alfirin

1. Maybe Denethor didn't start using the Palaintir until after Boromir left.

He first used it after his wife died, being depressed and worrying about his "line" as Finduilas died when his boys were still pretty young. However, we aren't told how often he uses it then, he definitely steps up the frequency of use after Boromir leaves, and even more after finding out Boromir is dead.

2. Rivendell may have been out of the Palantir's range.

Possible, that I do not know enough about Denethor's palantir to tell you. I do recall though that Denethor's palantir was oriented towards the East, as certain Palantir's could only look towards certain direction.

3. Whatever magic Elrond had that made Rivendell so hard to find may also have prevented it's being scryed by a Palantir.

This is possible too, but I would just suggest that determining the general location with a palantir is very hard. These weren't clear or crisp "pictures." Images relied on shadows and lighting, so if someone was trying to look into a room, but there were no lights, the person wouldn't be able to see anything. Also, remember that when Pippin uses the Palantir, and Sauron invades in, Sauron believes Pippin is in Orthanc, because he tells Pippin to give a message to Saruman. The problem is, Pippin is outside, and 100s of miles away from Orthanc by this time. Sauron had no idea that Isengard had been destroyed, nor that the stone had left Isengard and this guy uses the palantir a lot.

4. Comments made by Gandalf in his discussion of the Palantiri make me believe that a great will is needed to use the stone for DIRECTED viewing, without it the stone simply shows random images. Maybe Denethor didn't have that kind of will.

This one would be hard to tell. In UT: The palantir, Tolkien does write that eventually the Stewards to have the authority to use the palantiri. Part of being able to use the palantir, is 1st knowing how to, but 2nd is being the rightful owner. Aragorn, was a rightful owner, hence why he is able to best Sauron (who was not one) through the palantir. Denethor, as a steward, also was a rightful owner, also he was priviledged to top secret records about the palantir that only the Stewards, and their children, had access too - and from the UT we are told that while his father Ecthelion ruled, Denethor rummaged through all the records about the palantir. So, Denethor knew how to use it, and was a rightful owner.

However, you still have to have a significant amount of willpower to contend with Sauron, even though Sauron wasn't a rightful owner. Sauron nearly broke Aragorn, and Aragorn had the authority, plus he was much farther (the distance plays a factor as well, in UT, had Aragorn been closer to Sauron - as Denethor was - he probably would have been bested). Afterall, Sauron is a Maia, and for a mortal to challenge his will, well bad things are going to happen.

It is clear that Sauron was controlling the images Denethor was viewing, when he began doing this, I do not know, but I would imagine it wouldn't be long after he realized Denethor was peeking around. He would of course want to do anything to weaken his strongest enemy, and realizing that the Steward is poking around with the Palantir would be a good opportunity. Sauron could not make the palantir lie and show false images, but he could make it misleading and control what Denethor was seeing - he was only showing Denethor the massive amount of forces Sauron had, and the Corsairs a sailing in, leading Denethor to lose all hope.

Once Denethor lost hope, he thought his only chance was to challenge Sauron through the palantir, the "Lord of Minas Tirith vs. the Lord of Barad-dur" (see Appendix: The Stewards), and that is when he lost his mind.