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.)
Continuity mistake: At the Three Broomsticks, when Slughorn and Harry speak, Slughorn holds a silver mug with a high foam head, but in the shot facing Harry, before Slughorn actually spills the drink the mug's foam head is gone (visible at the bottom of the screen), only to reappear when he spills it on Hermione ,whereupon the same previous angle is shown again without the foam.
Continuity mistake: When Dumbledore and Harry first arrive in front of Slughorn's temporary residence in Budleigh, Babberton, Harry's height barely even reaches Dumbledore's shoulders (likely the actor's stand-in), but in the next shot facing them Harry's height compared to Dumbledore is back to normal, level with the Headmaster's eyes. (00:05:35)