For me, it was the portrayal of Denethor as cowardly and villainous. Denethor was never a "nice guy" even in the book, but he was much stronger and more honorable than he was portrayed in the film. While he gave in to despair at the very end, it was the result of his continued battle of wills against Sauron through the palantir. Faramir being mortally wounded finally drove him over the edge.
Likewise, I didn't like Gandalf beating up Denethor in the movie. Gandalf butted heads with Denethor, but Gandalf respected him. Having him physically assault a head of state in his own palace and get away with it just didn't make any sense to me.
And the soldiers of Gondor were like sheep. Denethor orders his son to be burned, and they blindly follow him. Gandalf lays the smack down on Denethor and yells at the soldiers to get back to their posts and they blindly follow him.
Aside from that, the only thing that bothers me is having the elves at the Battle of the Hornburg. The elves had their own battles to fight elsewhere. It was probably done to show that the other peoples of Middle-earth were fighting against Sauron, but the way it was done just doesn't sit well with me.
Anyway, what are your dislikes and why?