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.
Continuity mistake: When Snape is insulting Hermione on being a know-it-all while he is substituting for Lupin, he has a slide show running. The shot shows Hermione with the projector behind her. The projector now changes slides fully and stops moving. When the shot changed back to Snape, the slide is still changing. It could not be the next slide because the slide changes every few seconds.
Continuity mistake: When Hermione and the others are in Hagrid's hut, a rock with a swirl on it hits the pot. Later, when Hermione and Harry are reliving the scene from the exterior view, Hermione picks up the "same" rock to throw at the pot. The rock is different though, it has a bigger swirl on it.
Continuity mistake: When Harry collapses next to Sirius after the Dementors have been repelled, the ground where his head lands is covered in fairly small stones. In the following overhead shot of Harry and Sirius, there are some much larger rocks next to his head, and a patch of dirt with no stones is visible to Harry's left, where stones were before.
Continuity mistake: When Harry enters the room in the Leaky Cauldron that the Minister of Magic is in, Hedwig has arrived before him. The owl shown at the start of the scene is a white owl with many black spots on both its wings. However, when Harry leaves and Hedwig flies to his arm, this owl has very few spots at the edge of its wings and tail, obviously it's one of the other owls that portray Hedwig.
Continuity mistake: The cart with the TV changes its position in various shots. For example, in the close-up of Marge's legs lifting off the ground and when Marge floats out the door in the exterior shot, the cart is aligned with the doorway, then at other times it is at the inner edge of the draperies or in between.
Continuity mistake: When everyone, except Harry, leaves to Hogsmeade village, Hermione is waving as she and Ron walk directly behind McGonagall, with the last of the crowd of children ahead of them still in the courtyard. There is a short cut facing Harry now standing IN the doorway. Then the next shot from behind Harry, shows Ron and Hermione still walking past the fountain, but now McGonagall and the entire crowd of children are out of the courtyard. They could not have walked away that fast.