Continuity mistake: In the living room at the Weasleys' house, while Harry, Arthur, Nymphadora and Lupin are talking, in the shot facing Lupin, Harry's shoelace is untied. After a brief cut to a shot facing Nymphadora and Arthur (where we can see Harry's hands), it cuts back to the original angle and now the shoelace is tied. (This has nothing to do with Ginny tying Harry's shoelace much later on.)
Continuity mistake: When Harry is kneeling beside Dumbledore's body, at the foot of the Astronomy Tower, Ginny joins Harry and holds him at his left side (viewer's right). In the last close-up of Professor Dumbledore's face, Harry is visible in the background with a space to his left and Ginny is now gone. That same angle was shown before Ginny joined Harry.
Continuity mistake: In the dormitory, when lovestruck Ron is going gaga over Romilda, he is wearing a brown sleeveless tee shirt and its tan trim has many holes. When Harry brings Ron to Slughorn, Ron is still wearing that tee shirt, but now some of the holes are gone and the rest of the holes have changed position.
Revealing mistake: It is not what is seen here that is the problem, but what we don't see on the Hogwarts Express; first on the way to Hogwarts when Harry, Ron, and Hermione are in their compartment talking about Draco, and second, during holiday break, when Harry and Ron are talking about Unbreakable Vows. As the camera faces the large compartment window, we see the scenery out the window, but as the train speeds along, the scenic reflection of the windows opposite it, in the corridor, should be seen but isn't. What is reflected is the light colored wall of the compartment beneath the blacked-out window. The camera filming the shots from this angle is positioned at that window, and to hide the camera/crews' outline, the window was covered.
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.
Continuity mistake: In Potions class, when Hermione stands before the cauldron explaining what she is smelling in her closeup, we see Neville behind her with the broad space to his right (viewer's left), just as she says, "Spearmint toothpaste". In the instant cut to the wideshot, Harry is now shoulder to shoulder with Neville, too fast for him to suddenly be standing that close to Neville.
Continuity mistake: When Harry, Ron and Hermione are at the Three Broomsticks talking with Slughorn, Slughorn spills his butterbeer on Hermione and the table. Still in the conversation, the table is shown, but it's dry. Then a little later, there is foam on the table but only near Harry's glass. The rest of the table is still dry.
Revealing mistake: When Slughorn stands before Tom Riddle speaking of seven Horcruxes, as the professor faces the fireplace and says, "This is all hypothetical," and when Tom replies, "It'll be our little secret," in these close-ups particularly the square lighting/reflector screen becomes clearly reflected in the eyes.