Deliberate mistake: When Harry drops the Monster Book of Monsters, in the first shot facing Harry's feet as the book chomps at him, he runs backwards a few steps and he stands at the foot of the bed. However, in the shot facing the fireplace, there is actually plenty of floorspace now, much more than other shots, between the rug and bed for Harry to continue to run backwards.
Deliberate mistake: It was a deliberate directorial decision to change the geography of Hogwarts, but it still grates with continuity. Most of the Buckbeak scenes happen around Hagrid's hut, which is down all those steps and near the forest. However in the Philosopher's Stone, Hagrid's hut is about 5 seconds walk from one of the main entrances of the school, nowhere near a load of steps and huge hill. Also, the Whomping Willow (which itself differs greatly) is on the grounds of the castle, as you see it on flat land when Harry and Ron land the flying car in the Chamber of Secrets, however in this one it is right away from the school next to quite rocky land.
Deliberate mistake: During the DADA lesson with the Boggart, the body double for David Thewlis (Lupin) is quite evident in some close range, head on and side shots. As a matter of fact, Emma Watson's and other actors' body doubles are very noticeable in many shots not involving a stunt.
Deliberate mistake: The wings of the hippogriff are much shorter when folded up than when flying. According to the animators, the wings would have to be huge to carry the weight of the hippogriff when flying, but so big that they would drag on the ground when folded up. So they deliberately made the wings shorter.