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.
Revealing mistake: When Sid stabs Marc after he has transformed, there is no blood on the knife that he uses afterwards.
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: 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)
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.
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.
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.
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, as well as there being no stake in her hand when the vampire gets dusted. Not only that, but the mark isn't even close to the vampire's heart to begin with. (00:34:50)
Revealing mistake: As Willow, Cordy, Miss. Calendar and Giles are wheeled over the bones of the Master, Giles goes past and his hand brushes against the bones - the skeleton bends, revealing that it is rubber. (00:36:10)
Revealing mistake: When Buffy sets the vampire alight, his face suddenly gets very shiny, showing the fireproof gel that was applied to the actor's skin. (00:37:20)
Revealing mistake: In the scene where Absalom is speaking of the Anointed one, the line can be seen where the vampire makeup meets up with his real face. This may be seen in various scenes he is in.
Revealing mistake: When Buffy is fighting the vampires that are trying to resurrect The Master, at one point she is grabbed from behind by a male vampire and kicks a female vampire in a green top twice (right after Absalom shouts "The sacrifices! Stop them!"). If you watch closely, both of the kicks miss the vampire, revealing that the fight was choreographed. The punch that she delivers to the male vampire afterwards also looks fake.
School Hard - S2-E3
Revealing mistake: When Spike is talking to the Anointed One for the first time, one of the henchmen tries to rush him from behind and Spike backhands him without even looking, but Spike's hand movements, the reaction of the henchman and the sound of the punch connecting on the audio track are all out of sync.
The Dark Age - S2-E8
Revealing mistake: When Buffy and Giles are talking in the school in the final scene, the same extra (in a beige shirt and blue jeans) walks out of the room behind Buffy twice. (00:42:50)
Revealing mistake: Although the mirror in Buffy's room is mostly covered by photos, Angel's reflection can be seen for a split second as he walks past it to pick up the photo of Buffy ice-skating.
Revealing mistake: In the beginning of the episode, when Buffy stakes the vampire that she beats up for a long time, watch when she lifts the stake. The hole in the vampire's chest is a solid 8" below where she actually hit him with the stake. (It's an effects shot, so somehow, they just didn't line up).