Out Of Mind, Out Of Sight - S1-E11
Continuity mistake: When the gang are in the cafeteria and Giles comes along, Buffy's hands instantly change positions as she says "I love it when he says that!" Then, in the very next shot, a drink suddenly appears in her hand that wasn't there before.
Continuity mistake: When Buffy falls down after the Master bites her, you can see her fall, then hear her hit the dry ground. But then a few shots later she falls again and this time into water.
Continuity mistake: After Buffy finds Dr. Gregory's glasses at the start of Miss French's class and places them on the table, they move position twice throughout the rest of the scene.
Welcome To The Hellmouth (1) - S1-E1
Continuity mistake: The scene where Xander is on his skateboard, he becomes distracted seeing Buffy walk up the stairs and accidentally hits the pole. When the camera pans back, you can see Buffy is out of view, and is nowhere to be seen. Because she was still at the top of the stairs when Xander hit the pole, you should have been able to see her walking in the background.
Never Kill A Boy On The First Date - S1-E5
Continuity mistake: When the vampire breaks the glass with his head, the remaining glass disappears.
Welcome To The Hellmouth (1) - S1-E1
Continuity mistake: When Xander is talking to the girl at the Bronze his hand is on the pole and off the pole throughout.
Continuity mistake: When Buffy descends into the Master's lair, the way she is holding her crossbow changes depending on the camera angle. Sometimes it's pointed straight forward, sometimes it's pointed upwards.
Continuity mistake: When Giles and Jenny are talking about Buffy, Giles says "We must get in touch with this Brother Luca chap!" watch Giles. In the first shot he's still reaching towards the top of the cabinet. Instantly in the next shot, he's in the middle pulling something down from the top of the cabinet.
Continuity mistake: When Giles and Jenny are talking in the library, when Jenny closes the bible, the way she's holding it changes instantly between shots.
Continuity mistake: When Buffy is consoling Willow after she discovered the dead students, as Buffy leaves the room, Willow's mouth is open and she looks down. It then cuts to a wideshot. Instantly, Willow's mouth is closed and she's staring forward, and she looks down a second time.
Continuity mistake: When Jenny meets Giles after Xander's botched attempt at asking out Buffy, the way she's holding the folders to her chest subtly changes repeatedly between the closeup and wide shots.
Continuity mistake: When Buffy turns down Xander's date proposal at the start of the episode, throughout the scene, Xander has his backpack up around his right shoulder. However, when he walks away, it's instantly down by his side.
Continuity mistake: In the beginning, when Xander is practicing asking Buffy out with Willow, at once point Willow puts one of her snacks (candies, I think) into her mouth and starts chewing in a medium/wide profile shot of the two. It then cuts to a closeup of her and instantly she's no longer chewing, and immediately places a second candy in her mouth. She didn't have time to stop chewing and swallow between cuts.
Out Of Mind, Out Of Sight - S1-E11
Continuity mistake: When Cordy notices the word "Learn" in The Bronze and asks "What does that mean?" the positions of the ropes around her arms changes instantly between cuts.
Out Of Mind, Out Of Sight - S1-E11
Continuity mistake: When Buffy finds the invisible girl's "home" in the ceiling and picks up her flute, the position of everything on her bed changes between the initial closeup we saw and the shot of Buffy picking up the flute. Ex. In the initial closeup, the flute is on an open case, while in the shot where Buffy picks it up the case is closed. All the sheet music is in a slightly different position. A cylindrical object appears next to the flute that wasn't there in the initial closeup, etc.
Out Of Mind, Out Of Sight - S1-E11
Continuity mistake: When Xander makes the joke "Maybe it was a vampire bat!" in the cafeteria near the beginning of the episode, a sandwich suddenly appears in his previously-empty hand between edits.
Nightmares - S1-E10
Continuity mistake: When Willow goes down the stairs to the basement, as she reaches the bottom, she goes from looking forward to looking to her right between cuts.
Nightmares - S1-E10
Continuity mistake: When the Scoobies go to talk to Wendall about the spiders, when Wendall says "I don't know what to say about that " he instantly goes from looking forward to looking down between edits.
Nightmares - S1-E10
Continuity mistake: When Buffy's mom first wakes her up after her nightmare at the beginning of the episode, the positions of Buffy's hands, her mother's hand and the bed comforter all change between edits as it cuts from a closeup to a wide shot.
Nightmares - S1-E10
Continuity mistake: When Buffy goes to find Giles, who is going through newspapers, she asks him if he's found anything and he says "I don't know." Between shots Buffy goes from looking at him to glancing downwards with her eyes and then looking back up again between cuts.
Chosen answer: He had larangitis and because of the shooting specifications they had to have him shoot the scene with a bad throat, they then re-recorded his lines and dubbed them. At various points during the scene and indeed the episode you can see him touch his throat or rub it.