Revealing mistake: During the song-and-dance number "They Got The Mustard Out", if you look closely at the dancers, the man in green to camera right of the second row is horribly out of step with the music, and with the rest of the group. The spell makes everyone dance far better than they naturally would (Tara loses the clumsiness she often displays, for example), so it is a mistake to have someone under the spell dancing so badly.
Continuity mistake: When Buffy is singing "Something to Sing About", she sings the verse beginning 'All the joy life sends, family and friends', and we see that Anya and Tara are stood in the background, about 3 metres apart from each other. However, for one shot, they appear less than 1 metre from each other.
Continuity mistake: In the musical episode, 'Once More, With Feeling', when Buffy is singing her song in the Bronze, 'Something to Sing About', she breaks a pool cue over a demon's head. She holds the remains in her right hand and clubs another demon in the face with it, then the camera cuts to another angle and it's in her left hand when she stabs the next demon with it.
Audio problem: In the episode 'Once More, With Feeling', when Anya sings her first few lines of the song 'I'll Never Tell', you can still hear Xander talking about omelettes in the background, but for the last few lines he speaks (from 'I could do an omelette' onwards) you can see over her shoulder that his voice is dubbed.
Audio problem: In the final song "Where Do We Go From Here", you can hear Spike still singing even after he has apparently stopped. He and Buffy continue singing until after the line 'When do the trumpets cheer'. It is noticeable because James Marsters sings the word 'cheer' slightly out of sync with everyone else.
Revealing mistake: The knives Giles throws during Buffy's training are a very poor CGI job if you watch it in slow mo. All three knives Giles takes off the wall are identical, with a broad curved blade and a plain black handle. The first one has a transparent blade as it flies toward Buffy, then we hear it bounce off the far wall and it's way out of scale for the distance. The second knife has a diamond-patterned grip instead of a plain one. The third knife conveniently spins in midair for a second so Buffy can kick it out of the way.