Continuity mistake: When Buffy's fighting Spike at the end of the episode, there are times when it's obvious that it's James Marsters' stunt double. Spike's hair is platinum blonde, slicked back, and all one length in the back, while the stunt double's hair is more brassy, spiked in the front, and layered in the back.
Plot hole: Willow and Cordy disappear during a vampire attack. We later see that they spent the entire night hiding out in a closet, but wouldn't Buffy have gone looking for them once the vampires were gone? She knew they had run off somewhere (she mentions it to Giles when she gets a stake from the library). Instead she just goes home, leaving them still missing as far as anyone knows.
Revealing mistake: When Spike is talking to the Anointed One for the first time, one of the henchmen tries to rush him from behind and Spike backhands him without even looking, but Spike's hand movements, the reaction of the henchman and the sound of the punch connecting on the audio track are all out of sync.
Plot hole: When Buffy and Sheila are walking out of school after the meeting with Snyder, Xander runs up to talk to them. He mentions during this scene how Buffy will be helping out at the Parent-Teacher Night, but he shouldn't know this - Buffy only just found out about it in the meeting with Snyder.