Continuity mistake: When Angel and Buffy are sitting down talking about their kiss, Buffy picks up a coffee mug and holds it with both her hands. But in a wide shot shortly afterwards, she is no longer holding the mug and it has moved further down the table.
Continuity mistake: In Season One Finale, "To Shanshu in LA" when Wes is lecturing Cordy on wants and desires, the number of bites taken from the doughnut changes, in one instance it breaks in half, most visibly when Wes takes a bite from Cordy's doughnut on the angle change.
Continuity mistake: In the season one finale "To Shanshu in LA," near the end Angel is fighting Vocah in the mausoleum and Angel rips off Vocah's mask, revealing the maggoty face underneath. In subsequent shots of Angel from behind Vocah, you can still see the edges of the mask on his face.
Continuity mistake: When Faith is sitting at the window and looks at the piece of broken glass she used to torture Wesley, it has a different shape than the one she first takes to torture Wesley. When she drops it out the window it has its original shape again.