Character mistake: Giles picks up the potential slayer Chao-Ahn from Shanghai in Episode 7.12, "Potential". However, when she arrives in Sunnydale (Episode 7.14, "First Date"), the language she speaks is neither Mandarin nor Shanghainese (the two main languages spoken in Shanghai), but Cantonese, which is not widely spoken there.
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.
Revealing mistake: The entire scene where Buffy is experiencing accelerated time, shadows of trees move in the wind but never actually grow or shrink. Even over short increments of time, the sun can move shadows noticeably, and judging from the speed of the people around her, Buffy is in accelerated time for at least half an hour.
Factual error: When Buffy and Angel escape from Spike, Dru and the Judge they jump down into the sewer, then run all of five metres before going up the ladder to escape. When they come out of the sewer they are in a very open area with the factory nowhere in sight. They have not travelled far enough for this to be the case.
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.