Continuity mistake: In Innocence, when the Scoobies are in the library, Oz (I think) says for the crew to meet outside Xander's house a half hour later. Then we cut to Buffy strolling through Sunnydale High in broad daylight, then back to Oz's van outside the military base and it's last night again.
Continuity mistake: When Buffy wakes up she is wearing metallic nail polish, yet when she went to sleep previously, she has no nail polish on. Later in a scene where Buffy is dreaming about her night with Angel she has the nail polish on again, even though that took place the night before when she did not have her nails painted.
Continuity mistake: When Buffy is told that Angel has become Angelus, she mentions "I should have known. When I saw him at the house he was different", but her earlier conversation with him took place not at the house but at his apartment. This isn't just a strange turn of phrase - the scene was originally shot at the Summers house, but was changed to Angel's apartment for more emotional resonance.