Continuity mistake: When Willow shows up at Oz's house to talk, her hair keeps switching back and forth between being behind her back or in front of her shoulders.
Bewitched, Bothered And Bewildered - S2-E16
Other mistake: Joyce tells Cordelia to grab some bandages for Xander from the bathroom upstairs. Joyce and Xander are in the kitchen and there is a small corridor that leads to the stairs, but Cordelia goes around the other way leading to the living room. Fair enough, Cordelia made a mistake. She isn't that bright. But she returns with the bandages coming back from the living room. Why come downstairs and then go All The Way around through the living room when she could have just walked down the small corridor?
Deliberate mistake: After Jenny pushes the janitor's cart into Angelus and runs up the stairs, there's no physical way he could be waiting for her at the top of the stairs (even with vampiric speed). Joss Whedon has admitted in interviews that he put in this blatant continuity error as the situation is a staple of the horror genre (girl runs from villain, only to find him standing right in front of her).
Continuity mistake: When Buffy looks into the childrens' ward the sign on the door saying 'Basement Access' disappears and reappears between shots. (00:12:00 - 00:36:15)
Continuity mistake: While Buffy is in the hospital, they zoom in on the bedside clock changing from 2:26 to 2:27. In the next shot of Buffy, you can see the clock in the background and it reads 12:15.
Other mistake: In the basement when Death throws Ryan to the floor, Ryan lands pretty softly considering that he was just thrown pretty hard.
Other mistake: Buffy freaks out when she's first taken to the hospital. Joyce tells the gang it was because her cousin died when they were young, but in season one episode "Angel" Buffy has no problem being in the hospital, same with later seasons.
Continuity mistake: After drinking the water with the virus, Buffy looks into a room and her hair is damp and brushed back. In the next shot, it's dry and parted down the middle.
I Only Have Eyes For You - S2-E19
Visible crew/equipment: When Xander opens his locker and the gross hand grabs him, if you use slow-mo when the shot is inside the locker looking out, you can see the white t-shirt of the man whose arm it is. (00:10:20)
I Only Have Eyes For You - S2-E19
Factual error: In the episode 'I Only Have Eyes For You', during the flashbacks to 1955 James and Grace dance, and James later shoots himself, to the song 'I Only Have Eyes For You', which wasn't released until 1959. (00:18:20 - 00:26:50)
I Only Have Eyes For You - S2-E19
Revealing mistake: After Buffy has entered the wasp-filled school there's a shot of the others standing outside waiting for her. In the establishing long shot if you look closely you can see they used the same shot as earlier in the episode - Buffy is standing there with them. (00:34:10)
I Only Have Eyes For You - S2-E19
Visible crew/equipment: After the history teacher writes, "Don't walk away from me, bitch!" on the chalk board, Buffy says to Xander, "I'm telling you, something weird is going on." As she says "something", a boom mic is reflected in the window behind her on the right.
I Only Have Eyes For You - S2-E19
Continuity mistake: When Buffy is waiting in Principal Snyder's office, the 1955 year book slides off the bookshelf and lands open, but when Buffy walks over to pick it up, the book is closed.
I Only Have Eyes For You - S2-E19
Audio problem: When Giles looks through the window of a door at the high school and sees the janitor yelling at the teacher, the janitor's lips don't match with what he is yelling.
I Only Have Eyes For You - S2-E19
Continuity mistake: When George shoots Mrs. Frank, her body falls off the balcony headfirst on a closeup shot. She flips in the air once on her way down. But in the following wide shot, she flips in the air on her way down again.
Continuity mistake: When Willow is interrogating Jonathan, she makes a comment about how he resented being pushed around. In the first shot, she's facing him. It then cuts to the opposite angle, and she's facing sideways. Then, in the very next shot, she suddenly turns 180 degrees between cuts after walking by him.
Other mistake: After Gage turns into a monster and fights Buffy, the two monsters slide into an open grate. During the shot, there's some sort of weird "glitch" in the background where the garbage can and wall seem to slightly move. All I can assume is that a few frames were trimmed to speed up the shot and it may have exaggerated subtle camera movement, making the background appear to "jump" slightly.
Continuity mistake: When Buffy, Willow, and Cordy are talking at the swim meet (after Gage waves at Buffy), the way Buffy is holding her hands changes back and forth between two positions as it cuts between her and Cordy. Seems two different takes were used, and she had her hands in slightly different positions in them.
Answer: She has superpowers, ergo fast movement. The reason she outruns him so easily in "Touched" is that she stops trying to actually fight him and just dodges instead.
Shay