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.
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.
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.
Continuity mistake: When the earthquake happens at the start of the episode, and we see the Master celebrating, his hands instantly change positions at least twice between cuts. (Sometimes it matches perfectly between cuts other times they're in an entirely different position between cuts).
Continuity mistake: When Cordy stops kissing her boyfriend and says "What was that?" at the beginning of the episode, the lighting on Cordy's face changes completely as it cuts between the two camera angles. In the first angle, the lighting is much darker and shadowy, while in the second angle, her face is suddenly much brighter.
Continuity mistake: After Buffy cuts herself out of her chair, she unties Cordy's left wrist. The scene cuts away to Giles, Xander, Willow and Angel. When the scene cuts back to Buffy and Cordy, suddenly Cordy's wrist is tied again. There's no indication that it was retied in the meantime.
Continuity mistake: When Cordy and Buffy are tied up, at one point Marcie the invisible girl punches Buffy. As it cuts from a closeup of Buffy back to a wideshot, the position of Buffy's head and the expression of her face instantly changes between cuts. She goes from having her head crooked with a pained expression and her eyes half-shut to having her head straight with a shocked expression and her eyes wide open.
Continuity mistake: When the invisible girl pushes Buffy, and she falls through the ceiling and onto a table, the position of Buffy's arms changes slightly between edits when it cuts to a high-angle shot of her knocked out. Some of the debris around her also changes position.
Continuity mistake: This is subtle and hard to notice. When Buffy is explaining that something bumped into her in front of the school after Giles explains what it's like to be touched by a ghosts, pay attention to Xander. In the first shot, he's standing about two feet back from Buffy and his left shoulder is behind Willow. In the next shot he's suddenly much closer to Buffy and Willow is no longer in front of his left shoulder.
Continuity mistake: In the beginning when the Scooby gang and Giles are talking in the cafeteria and Giles asks Xander to help him, in the first shot Xander doesn't have his hand on his drink, but when the shot cuts to the opposite angle, suddenly he has his right hand grasping the dop of his drink.
Continuity mistake: When Buffy is checking out the locker room after the credits, she starts to close one of the lockers. It cuts to the opposite angle and the locker is All The Way open, and she starts to close it a second time. The way she's holding the locker door also changes instantly between edits.
Continuity mistake: In the beginning of the episode, when Cordelia's date is in the locker room and he talks to two other students, pay attention. There's a combination lock and a baseball bat on top of the lockers. They change positions repeatedly between cuts, getting closer and further apart almost at random depending on the shot.
Continuity mistake: When the school-bell rings at the beginning of the episode after Cordelia talks about hitting the girl on the bike, in the first shot Willow is just starting to put her book into her backpack and is still seated. In the next shot, Willow is suddenly starting to stand up and has already put her book away.