Character Problems: 1) Every scene in which we see Professor Snape is either played for comedy at the time or played for comedy later on in the movie. I was hopeful that there might be one scene that was not played for comedy, that is, when Snape says he knows Harry has been going through his private stores, but this too was used for comedy later on when Dumbledore turns to Snape after discovering Barty Crouch Jr. and says, "Now I guess we know who's been going through your stores, Severus," or whatever it is he says. Again comedy. Snape can be funny. I enjoyed the humor that he provided earlier in the movie, but I have to wonder what in the world they are going to do when they get to movie number 6.
2) They had several shots during which it is hard not to imagine a romantic tension between Harry and Hermione and they totally loused up the romantic tension between Hermione and Ron after the Yule Ball. She's not supposed to be as angry at him for getting in the way of her date with Krum as she is angry at him for not asking her to the ball himself and then sulking about it. And Harry agrees with her. Now, I know in the book, Harry just thought that Hermione was right and didn't say anything, but they could have really played that off better somehow in the movie. If Harry and Hermione ever kiss in these movies, I will not spend another penny on going to see them.
3) The actor who plays Dumbledore has not read the books. I would be willing to bet a good sum of money on this if I had any. The scene where Dumbledore comes after Harry after his name comes out of the goblet was way overacted. Dumbledore actually grabbed him and shook him while screaming. This will not get in the way of the later plot as much as the previous two issues, but I think it was a bad decision. Dumbledore would never endanger a student or be physically threatening to them in any way. The core motivation of his character is care for the students he teaches.
Theme Difficulties: The movie left out any part of the book that had to do with the strong persecuting the weak. It left out the fact that the death eaters did not in fact burn down the entire Quidditch camp. They did something which defines who they are much more clearly in the book. They tortured a muggle family. Also, there were no house elves in this movie. In the book, they play a major role, and along with the house elves, they left out everything about S.P.E.W. (Hermione's quest to create the Society for the Preservation of Elvish Welfare).
They did a similar butchering of the themes of book three by leaving out the fact that Harry's father is the same as Harry's patronus. They also took out a lot of the themes having to do with family in the third movie.
Plot Difficulties: My main problem with the plot is that they never even touched priori incantatem until the very end and at that point they only said the name. Anyone watching the movie who hadn't read the books would have no idea that, although this casting of it is spectacular, it is a normal spell that anyone can use to determine the last spells cast by any individual's wand.