Continuity mistake: In the scene when Spike was in Buffy's kitchen with Joyce, Buffy keeps him down on the table and grips Spike by the throat. She uses her left hand (in the close shot it is also the left hand) but in the next scene when Angel is also in the kitchen and Spike hits Buffy's hand, she uses her right hand (Spike hits her right hand).
Other mistake: In the final scene, where Spike drives down the road while singing 'My Way' he turns the steering wheel significantly, but in the external shots the car is travelling down a straight road, with no bends. He is turning it sharply to the right as the camera cuts to outside, but the car continues straight ahead.
Continuity mistake: In the scene where Xander and Willow are stuck in the factory Xander wakes up you'll notice that the blood on his side burn closest to his ear constantly changes lengths from shot to shot. It goes from under the chin to slightly below where the blood on the other side of his side burn is.