Revealing mistake: As Willow walks through the forest pursuing Warren, just after we first see Warren running, there's a shot of Willow walking into a bit of a clearing. Her shadow crosses a tree on the right (could be caused by the moon), but then a couple of seconds later another shadow is visible on a tree to the left - obviously an artificially lit forest.
Continuity mistake: At the end of the episode when Buffy is talking to Giles about how she can't face her friends, her hair is over her ears for the entire conversation, but when she is about to walk away, her hair is suddenly tucked behind her ear and she couldn't have tucked it behind as that side of her head is still in view when the camera's on Giles.
Continuity mistake: When Buffy is giving her speech about being chosen, there is a shot of Andrew sitting on the couch next to Xander and Anya, but in several of the shots of the Potentials he can be seen standing on the other side of the room in front of the curtains. It's definitely him - his face isn't visible, but the clothes are the exact same.
Continuity mistake: According to Giles in 'Revelations' there are 12 cemeteries in Sunnydale, but in 'Becoming Part 1', amongst others, Buffy agrees to meet someone (Angelus in this case) in 'the cemetery'. If there are 12 in the city, how would they know which one she means?
Plot hole: When Buffy talks to Xander at the end and he tells her to stay with Riley, she mentions that he is going at midnight. But earlier in the episode, Riley doesn't tell Buffy he is going at midnight, he says "Transport's leaving tonight" first, and at the end of the conversation he says "Unless you give me a reason to stay, I'm leaving tonight". Nowhere in this episode does he tell Buffy that he's leaving at midnight.