It is of course impossible that the movies could be completely faithful to the books. This is never possible with movies taken from books, some things don't film well, others film too well (like the Balrog, which is left more to the imagination in the book). Film is inherently third person objective, which very few worthwhile books are written in (none, in my opinion). Third person omniscient and limited omniscient, and first person particularly don't translate well to film, because there is too much that simply cannot be portrayed. And the "transmitted epic interpolative narrative" style of Lord of the Rings is completely lost in moving the work to film.
In some ways it is even impossible to expect that the movies would be faithful to the spirit of the books. After all, Tolkien was a deeply commited religious thinker, and his books are deeply Christian and, in fact, Catholic works. The director and actors of the film largely subscribe to interpretations imposed on the work in the seventies, many of which are diametrically opposed to the attitudes that permeate the books. For instance, Tolkien regarded the Ring of Power as symbolic of totalitarian socialism, whereas the seventies regarded it as a symbol of nuclear power.
And I have to admit that there were artistic decisions that had nothing to do with underlying philosophical outlook that set my teeth on edge. For instance, the Nazgul come across as very weak in the film, and with just slightly more faithful adherence to the books, a couple of lines of dialogue to explain things, that would not have been the case. For instance, if Aragorn had specified that he didn't drive them off, they simply left because their purpose was achieved with the Morgul blade, then they would have remained terrifying without his heroism in fighing them being lessened (in fact, it makes his heroism greater knowing that he went in against a foe he knew himself helpless against). Also, it would have been natural for Frodo to ask, upon waking in Rivendell, if the Nazgul were dead (as he did in the book). Then he could be told that they were only dismounted, that no power of the Elves or Gandalf himself could serve to actually kill them.
There are elements in which the portrayal of Moria fails as well. In the book, it is clearly explained that one reason Gimli has come to Rivendell is to seek tidings of his kin in Moria. That exlains why he wants to visit there. By the same token, Boramir has come seeking Isildur's Bane. Legolas brings tidings of evil things in Mirkwood as well as of Gollom's escape.
Of course, not everything could be included. But there were times that I felt that five minutes of critical dialogue had been cut in favor of ten minutes of very pretty scenery. All well and good, for those of us that have read and re-read the books, but not so good for those that don't know what a Nazgul is, or for those that understand little of the history of Moria and the many battles the Dwarves fought against Orcs and trolls in its labyrinth.
The battle in Balin's tomb was a perfect example of doing things both right and wrong. Having Pippin's contrempts with the well be more egregious and immediate was a good idea. Having the inital fighing take place in a room with only one entrance and exit, rather than one entrance for the orcs and a seperate exit for the fellowship, was a mistake. Also, in the book once they have fought the orcs in the tomb chamber and retreated through the other doors, Gandalf seals the entrance with a spell. He first encounters the Balrog when it challenges his spell and destroys the doorway in the process. This gives them breathing space to make for the bridge, where they meet the Balrog again and realize its true nature. The way it happens in the movie is visually stunning, but tactically nonsensical.
I could go on all day about how I would have done things differently, but the fact is that Lord of the Rings was still a great movie. Middle Earth comes alive, and if it is inexplicable at times and unlike Tolkien's vision, it is still breathtaking in sweep and scope. It truly is a worthwhile movie, and I hope that it will inspire another generation to read Tolkien's work.