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. (01:26:50)
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. (00:34:35)
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: When Hagrid and Slughorn are drinking after Aragog's funeral, Slughorn's cup is considerably larger than Hagrid's (an effort to show size difference between Slughorn and Hagrid), and note when Slughorn holds his cup how large it is compared to his hand. But after Hagrid passes out Slughorn's cup is now the same size as Hagrid's cup - Slughorn's hand is resting on the table right beside the cup, which is now significantly smaller compared to Slughorn's hand. (01:50:05)
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.
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 finds Hermione crying at the bottom of the stairs, with the conjured canaries flying overhead, there are numerous leaves/debris on the lowest steps and near her feet, but in the shots looking down from the top of the stairs the area is clear. (This has nothing to do with the few leaves that blow about.)