Continuity mistake: When Harry goes to the table to clean up Marge's broken glass and when he stands at the counter as Marge blows up, there is a large rug in the kitchen, under the center cart, whose edge reaches the counter stools. When Harry storms downstairs with his trunk, Petunia and Dudley stand at the kitchen doorway and the rug is gone - it would be visible if it was on floor. (Likewise, the rug was gone when Marge and Ripper arrived, but it could be presumed that the rug was laid out before their meal.)
Audio problem: When Cornelius Fudge says, "Oh yes, indeed, indeed." near the end of the movie, his mouth doesn't move.
Continuity mistake: When Marge floats out the patio door in the exterior shot her jacket lies flat over her skirt. In the next shot Vernon shouts, "I've got you Marge," as he grabs hold of her hands, and the bottom of her jacket is way up by her arms - note the blazer lining and her blouse. However, in the next shot the jacket lies straight and flat once again.
Continuity mistake: During Hagrid's lesson, when Harry walks towards Buckbeak as Hagrid explains to Harry that he needs to wait for Buckbeak to bow back, etc., in the next shot a boy on the left of the screen drops his cloak to the ground. In the next shot of the students, the boy has it on his arm again, but in the next shot as Harry bows, it's on the ground once again.
Other mistake: When Harry is talking with Arthur Weasley at the Leaky Cauldron, the number '301' (colored in white) digitally pops up right underneath the wanted poster. The composite people neglected to remove it. Sirius Black's number is '390' (colored in black) - it's written on the paper that Sirius holds in the poster.
Continuity mistake: When Harry lifts the lid in the Honeydukes cellar, in the first shot there are two gold pots, small and large, beside the table directly in front of him. Of course in the next shot, as the man climbs the stairs, only the short gold pot is beside that table. In the next shot, as Harry climbs out, the two pots' positions differ.
Continuity mistake: After Harry leaves the Dursleys, Sirius the dog shows up behind a park bench surrounded by dimly lit thick bushes. When the Knight Bus arrives, the bench is visible across the street and now it's brightly lit and the trash container beside the bench is clearly visible. Then, before Harry boards he has one more look at the bench and it is just as dark as the first shot.
Continuity mistake: When Hermione says, "Awful things happen to Wizards who meddle with time, we can't be seen," in the shot facing her she places her right elbow up on the pumpkin. In the next shot facing Harry her arm is down on her lap, yet in the next shot facing Hermione her arm is up again.
Continuity mistake: As Lupin packs in his office, the gramophone and books on his desk are visible in many shots. When Harry first walks in, the set of three thin books, bound with a string at the top of one pile, as well as the gramophone and other books noticeably change their position in quite a few shots.
Continuity mistake: Before Hagrid's lesson begins, Malfoy yells, "Dementor! Dementor!" and they all spin around. Ron and Hermione stand beside one another in the first and third shots, yet in the middle shot facing Malfoy, they're a good distance apart. As a matter of fact, in most shots throughout this entire scene many of the students' positions and actions change and/or shift back and forth in consecutive shots, some quite drastically.
Continuity mistake: On the Hogwarts Express, Lupin pulls out his wand to repel the Dementor attacking Harry. In the shot facing Lupin his shirt sleeve is mostly covered by his suit sleeve and he holds the wand a particular way. In the next close-up facing the Dementor, Lupin's arm is visible and a much greater area of his shirt sleeve is now seen and he holds the wand completely differently.