Continuity mistake: When Veruca comes to Oz's cage to spend the night there, she tosses her jacket onto the round stone thingie (knob?) at the end of the stairs, and it covers the whole thing. However, when Willow discovers them in the morning and Veruca goes to pick up her jacket, you can see that it has moved. Willow didn't touch it when she entered, and both Oz and Veruca were locked up so they couldn't get anywhere near it.
xx:xx:xxGrigory the Wanderer
Factual error: When Giles and Cordelia are driving to save the girls from getting burned at the stake and are making the potion to make the demon show his true face Giles tells Cordelia to shred the Wolfsbane. This is a huge mistake as any Witch will know (my sister pointed this out to me) that Wolfsbane is highly poisonous and should never be touched with bare hands and Cordelia didn't have gloves or anything.
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Revealing mistake: When all the vampires are saying "for the dark", and one gets staked, there's a mark on his shirt where the stake's about to come through before it actually happens. Plus Buffy's hands are in the wrong place for her to have pushed that stake through anyway. Not only that, but the mark isn't even close to the vampire's heart to begin with.
Continuity mistake: When Xander is showing Willow and Buffy his fake ID and the view of the shot is from behind Xander, he is holding the card with his thumb and middle finger. Switch to the view from behind Willow and it's being held with his thumb and index finger. Then it switches to behind Xander again and it's back to thumb and middle finger.
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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.