Revealing mistake: When Sid stabs Marc after he has transformed, there is no blood on the knife that he uses afterwards.
Nightmares - S1-E10
Revealing mistake: The Master's artificial thumbnail is visibly falling off in a few shots of the opening teaser. (00:01:30)
Nightmares - S1-E10
Revealing mistake: When Xander punches out the evil clown if you freeze-frame you can see the punch missed the clown by quite a distance, I noticed it without freezing it but it's better to see if you do. (00:35:35)
Revealing mistake: When Buffy breaks into the locker, the locker is already damaged. Probably from a previous take.
Suggested correction: Watching the scene, the only real damage is a slight dent that isn't all that close to the lock (she basically punches out the lock to open it). And to be perfectly honest, a dented locker isn't out of the ordinary for a high school. I saw plenty of dented, bent and damaged locker doors all the time back in high school. It's entirely probable that it is damaged from a previous take, but I think it's also within that sort-of realm of possibility (since like I said, dented lockers aren't out of the ordinary) that it might not be considered a mistake. I'll leave it up to people's votes.
Nightmares - S1-E10
Revealing mistake: When Willow opens the door to the basement to look for Buffy, the shot looking up the basement's staircase shows Willow's shadow on the inside of the door. In the previous shot when she opened the door, it opens towards a wall and a staircase to the second floor. But there is no light source coming from the wall or the staircase, giving the impression that the basement was filmed on a separate set.
Revealing mistake: When Willow says "The usual " at the beginning of the episode and it cuts to Buffy landing on the ground, you can briefly but see the stunt woman playing Buffy's face in the first shot for a solid second or two. That definitely isn't Sarah Michelle Gellar.
Out Of Mind, Out Of Sight - S1-E11
Revealing mistake: You get a pretty fast but noticeable glimpse at the stunt-woman's face when Harmony is pushed down the stairs, and it's obviously not the actress.
Welcome To The Hellmouth (1) - S1-E1
Revealing mistake: When Buffy sneaks into the locker room and checks out the dead body, you can see part of the outline around the prosthetic vampire bite on his neck (it isn't quite blended in properly), revealing it's an appliance.