Other mistake: In quite a few shots during the film, it is much too obvious that there are no lenses in Harry's glasses, whereas in previous and following shots the glasses have lenses. A couple of instances are: when Harry drinks the Felix Felicis and when Harry kneels beside Dumbledore, at the foot of the Astronomy Tower.
Other mistake: In the film Harry Potter and the Half Blood Prince, Professor Slughorn (during one of the 'Slugclub' meetings) asks Hermione what her parents do for a living, she replies, 'They're Dentists.' Slughorn and the other wizards stare blankly, not knowing what Dentists are. However, in the film 'Harry Potter and the Chamber of Secrets' in the burrow, we see the magical clock that shows the family's whereabouts, and we see that there is a section marked 'Dentist'.
Other mistake: When Harry and his friends visit the Weasley's house the second time - when the Death Eaters attack - the constellation Scorpio is visible in the sky. Scorpio is a summer constellation. It shouldn't be visible in the winter. Furthermore, it probably can't be seen as far north as England (although I don't live there, so I'm not sure).
Other mistake: When Professor McGonagall is talking to the trio about the necklace incident and Professor Snape is walking by in the background, he stops just before she calls him over.