Now that I've seen this movie twice, I feel qualified and ready to discuss it. Anyone who hasn't seen the movie and/or read the book and plans to do so, please skip this particular entry, as I will be discussing certain plot points and would thus be "giving away" part of the story.
I have to start by saying that I liked this movie a great deal. It's the best of the bunch so far, in terms of actual movie quality. By that I mean that the acting, film direction, cinematography, etc. were all better than they were in the first two. The first two basically attempted to just transpose the books into film. I like that on a certain level, but the books are getting longer, and the first two movies were already well over two hours each. At some point, different tactics needed to be used, or else the films were going to start being prohibitively long.
Actually, in thinking about this movie, I have to wonder how successful they're going to be in turning the rest of the books into films. All of the remaining books are or will be considerably longer than Azkaban, and yet already this one feels rushed. Probably every criticism I have of this movie comes back to that: things from the book often had to be sped up or left out completely in order to deal with time constraints.
My most major beef deals with the omission of a major plot point surrounding the Marauder's Map. No explanation is given as to how Professor Lupin knows how to operate it--anyone who has read the book knows that he in fact helped to write it. This isn't that important in and of itself, but the entire related subplot was left out, and that does seem important. The fact was that Lupin is a werewolf, and when he was at Hogwarts his friends became Animagi (shape-shifters, essentially) in order to be with him and help control him during the full moon. That's important because Sirius Black and Peter Pettigrew were two of those friends, and no one knew they were Animagi (because it was illegal to become one without registration, so they kept it hidden), which allowed both of them to hide for so long. This also touches on the stag form that Harry's Patronus charm takes on toward the end of the movie--his dad's Animagus form was a stag, but this was never mentioned. It was never clear that Black, Pettigrew, and Lupin were all part of the elder Potter's group of friends when they were at school.
On one hand, I think that anyone seeing the movie without reading the book can probably do without all that information. It doesn't make this particular movie that much less enjoyable, at any rate, although I personally would have been wondering how everyone knew about the damned map if I didn't know from reading the book. My main concern is how they're going to deal with these plot points if they come up in future films. It seems impossible that they can continue to leave this stuff out, but maybe they can.
These movies have a fine cast, but sometimes it seems as though the actors are somewhat wasted with as little screen time as they get. Maggie Smith as Professor McGonagall had what amounted to little more than a cameo role in this film, and Alan Rickman as Professor Snape always deserves more screen time. Emma Thompson did an incredible job as Professor Trelawney, but didn't get to portray some of the better moments in the book. Hopefully she'll be back for upcoming films.
All of that being said, this movie did a lot of things right. It was considerably darker than the first two films, but that darkness was offset with an injection of humor. The acting was great--I singled out a few performers, but the kids in the main roles (Dan Radcliffe, Rupert Grint, and Emma Watson) have really gotten a lot better. Also, this film incorporated several "mood" shots that have been absent before--flowers shrivelling and dying as the dementors pass, and several scenes that incorporate clocks and time. Pretty cool.
Overall, I would have to say that the film was quite well done, but could have been even better. I'm very interested to see what they do with the coming films, but Prisoner of Azkaban set the bar pretty high. If they don't continue to improve, I'll be pretty disappointed.