Revealing mistake: When all the vampires are saying "for the dark", and one gets staked, there's a mark on his shirt where the stake's about to come through before it actually happens. Plus Buffy's hands are in the wrong place for her to have pushed that stake through, as well as there being no stake in her hand when the vampire gets dusted. Not only that, but the mark isn't even close to the vampire's heart to begin with.
Continuity mistake: In the season two episode, 'When she was bad', in the scene where Buffy smashes the masters skeleton with a sledge-hammer she smashes the rib cage to pieces. Suddenly the rib cage has again become completely intact and she smashes it to hell again.