Most Hated Part: Practically the whole
Two Towers.
More specifically...
The Fellowship of the Ring: This was by far my favorite of the three. The alterations in this movie were (for the most part) at least reasonably explicable. I still don't understand why Jackson had to make Gandalf the one who was afraid to go to Moria rather than the one who inspired it. The more I see it I am also getting less and less impressed with Jackson's interpretation of the Nazgul. He made them really buffoonish and ineffectual. The part where they are literally riding right on top of the hobbits and can't seem to catch them is really hard to swallow. Of course, on the other hand, Tolkien said that the Nazgul had no great power over the fearless, but still... He also took a page out of Bakshi's movie and turned the Council of Elrond into the Council of Babel (or rather Babble). Galadriel: need I say more?
Oh yes, and the winged (and oversized) Balrog.
Other than these things I found the movie to be pretty enjoyable.
The Two Towers: There is not enough time for me to say all the things that I hated about this movie. Even standing on its own without any reference to Tolkien's work (which I believe is how the script was written) I don't think this movie is any good. Most of the changes were utterly senseless and sabotaged the plot. Even in the midst of all this wreckage, there are a few monstrous warts that stand out for abuse. The entire sequence from the time Theoden decided to go to Helm's Deep until the battle begins is just awful, awful, awful. I don't find there to be a single enjoyable (or even coherent) moment in this bit until the fighting blessedly starts. Then, thankfully, all the annoying pointy-ears die (a just fate for having horned into the plot where they don't belong). The entire sequence from the time Faramir captures Frodo and Sam until the end of the movie is just awful, awful, awful. We witness the savaging of not only Faramir's character but Frodo and Sam become deceitful little sneaks (no wonder Faramir was so suspicious of them). We are also treated to more ineffectual blundering by the Nazgul. Osgiliath: need I say more?
A minor thing, but one that annoyed me, was that Grishnakh and his band were from Isengard and not Mordor.
The Return of the King: I have a fairly positive opinion of this movie, although part of it is probably that it is so much better than
The Two Towers. King Elessar the Bloodthirsty Maniac has already received the flogging that is his due. Then there is the Anduril thing. The whole Witch-king vs. Gandalf sequence was just terrible. I was also not too happy with the way Denethor and Gondor's "war preparations" were portrayed. Every time that Gandalf is riding to safety shouting "Get the women and children out!!!" makes me want to scream. I was also not happy that the Orcs broke into two or three levels of the city. This also relates to my disdain for the WK vs. Gandalf bout. I realize Jackson was trying to amp the tension, but once the orcs broke through I found the tension was shattered and the disappointment of defeat set in. It would have been much better to have the confrontation that is in the book. Frodo and Sam and Gollum: need I say more?
I was also passingly annoyed by that inane speech by Gandalf about how "death comes to us all." Well, in Middle-earth, no it doesn't. Gandalf himself only came to it by happenstance not biological imperative.
On the whole, I think most of the problems I have with Jackson's movies stem from his inability to break away from his horror film background and his compulsion to try to cram as much drama into scenes as possible to the point they become unbelievable and almost laughable (several instances of this with the Nazgul).