Continuity mistake: Willow is turned into a ghost. Throughout the entire episode, she can't touch anything (can't turn the pages of a book, etc.), yet towards the end when she and Giles go to Ethan's shop, and she leaves, you can hear that she opened and closed the door, even though she can walk through walls and can't actually touch the door. The curtain moves when she leaves too.
Continuity mistake: Towards the end of the episode whilst Buffy is fighting Caleb with the scythe, right after he says to her, "You're not slipping out of this fight, girl. Can't you see? You can't stop me. I can just keep going back for more. It's like being reborn," and throws her into a wall, the position of the scythe changes constantly between shots.
Continuity mistake: Sunnydale apparently has docks ('Consequences' and 'Surprise') and is quite close to a beach ('Go Fish'), but when Sunnydale is destroyed in 'Chosen', we see an overhead shot of the crater and it appears to be in the middle of the desert, far from any coastline.
Continuity mistake: After Buffy decides not to take the antidote to the demon's venom, we cut to a scene at the mental institution. She says she wants to go home with her mum and dad. As she says this her dad puts his hand on Joyce's left arm. In the following shot, Joyce suddenly has her right hand on top of his when it wasn't in the previous shot.