Other mistake: Joyce tells Cordelia to grab some bandages for Xander from the bathroom upstairs. Joyce and Xander are in the kitchen and there is a small corridor that leads to the stairs, but Cordelia goes around the other way leading to the living room. Fair enough, Cordelia made a mistake. She isn't that bright. But she returns with the bandages coming back from the living room. Why come downstairs and then go all the way around through the living room when she could have just walked down the small corridor?
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.