Visible crew/equipment: After Crookshanks runs off with Fred and George's Extendable Ears the twins apparate and startle Molly, and when it cuts to Molly asking Harry if he's hungry, the actor's L-shape tape mark can be seen on the floor behind Arthur. (Only visible on fullscreen DVD). (00:15:00)
Character mistake: In the scene just before Harry and Cho kiss in the Room of Requirement, there is a clear Daily Prophet headline to the right of the mirror - 'Mystery Disappearences' a mis-spelling of the word disappearances.
Continuity mistake: Right before Harry enters the courtroom for his hearing, we see a close-up of his face and the ends of his eyebrows (closest to the nose) stick out. In the next scene, when he sits in the chair, they have been cut back slightly. (00:19:50)
Continuity mistake: After the Weasley twins fly out of the school on their Broomsticks, when the students gather and applaud them, in the shot facing Flitwick, Nigel is standing to Harry's left, right beside him. In the shot facing Harry, Nigel is now standing a few feet away, to Harry's right. (01:33:40)
Continuity mistake: When Harry is talking with Hermione and Ron inside the room at the Black's house, in one shot Hermione's hair is covering the left side of her polo shirt, next shot you can see the logo because her hair is on her back. Seconds later, her hair is again covering her logo shirt. (00:13:00)
Plot hole: Harry can now see the thestral creatures because he witnessed Cedric Diggory's death in "Goblet of Fire." However, he should have been able to see the thestrals after Professor Quirrell died from Harry's touch in "Philosopher's Stone". Quirrell crumbles into dust (dying) while Harry is still conscious, watching, and fully aware of what he is seeing, thus allowing it to fully sink into his consciousness. Harry faints "after" Quirrell is dead and as Voldemort's spirit passes through his body. Nor does it only have to be a friend or loved one who dies before the thestrals can be seen - it can be anyone, including an enemy like Quirrell. There only has to be an emotional response to the death, which can be love, hate, fear, shock, etc. (In the book, Harry did not see Quirrell die, but that's irrelevant to the film).
Continuity mistake: In the Forbidden Forest, Hermione dings the bell on the handlebar in the close-up as Grawp stands quite a few feet away with empty hands. Harry's and Hermione's eyes remain fixed on Grawp as Hermione dings the bell, so we know he does not pick up another handlebar. In the next shot, Grawp, still standing in the same place, dings the bell on the same handlebar; it changed hands between shots.
Continuity mistake: When Lord Voldemort is coaxing Harry, Dumbledore appears in the fireplace and his side hair is behind his shoulders. In the next shot it hangs down in front of his shoulders. Then, as the fight between Voldemort and Dumbledore starts, his hair is behind him again. (01:53:40)