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.
Continuity mistake: When Buffy meets Angel, Angel is walking down the alley and Buffy swings around a pole and kicks him from behind. Except you can tell in the first shot that Angel is too far ahead of her - she couldn't have reached him to kick him. She's only able to reach him through the power of editing, as the shot cuts, and he's suddenly closer to her. She also somehow flips backwards yet lands in front of him. The scene looks cool in motion, but makes absolutely no logistical sense if you watch closely.
Continuity mistake: In the beginning, when Darla and the boy break into the school, the boy breaks through a window, reaches in, and unlocks the window from inside. When he does this, as the shot changes, the broken glass around the window changes slightly between cuts. (Noticeably, the glass wedged between his hand and the window vanishes.) Additionally, in the first shot, there's a microscope right next to the window, about an inch away. In the next shot, it seems to have moved about four inches to the left.
Continuity mistake: When the Master first starts to appear, rising out of the pool, the top of his head is wet. But in the next shot (a wideshot) where you see him continue to rise, he's bone dry. This is because in the first shot, the actor is really coming out of the liquid, whereas in the next shot, he's added through visual effects. He obviously was supposed to look "dry" the entire time, but because the first shot was done with an actor rising out of the pool on-set, there was no way for him to emerge dry.
Continuity mistake: When Jesse asks Cordelia if she wants to dance at the Bronze, and she replies "With you?", she goes from facing downwards to facing sideways towards Jesse between cuts. They try to hide the continuity mistake with editing (cutting the shot as an extra is partially obscuring the frame as he walks by), but you can see clear as day that she goes from looking down to looking sideways instantly.
Continuity mistake: When Buffy meets Willow at the Bronze, a drink basically magically materializes in Buffy's hands at one point. She points to the bartender like she wants a drink, but a few shots later (when she says "How come?") she suddenly has a drink in her hand without having picked it up in any previous shot. She also goes from not sipping her drink to sipping it between cuts just a few shots later.
Continuity mistake: When Buffy meets Willow at the Bronze, when Willow says she thought Xander was going to be there, Buffy is standing about a foot away from the bar and her arms are by her side. But suddenly in the next shot, she's right up against the bar and leaning on it with her elbow. Then in the next shot, she's about a foot away again.
Audio problem: When Buffy meets Angel, when she says the line "What I want is to be left alone!" and Angel replies "You really think that's an option anymore?" pay attention. Buffy's last few words don't quite match her lip movements, and Angel's lips don't seem to be moving at all for his line. The audio looping is a little sloppy. This is better seen in the brighter HD remaster, but is also noticeable in the original, darker standard definition master.
Continuity mistake: This is hard to describe. When Buffy and Joyce are talking in her room, Joyce keeps pulling pillows off Buffy's bed and re-arranging them. However, at one point, when the shot cuts back to her, she's holding a different pillow than in her last shot. This technically wouldn't be a mistake since she's off camera except in the shots facing Buffy, there's a mirror behind her with her bed in view, so we should have Joyce put down the first pillow and pick up the second one... and we don't.
Visible crew/equipment: When Buffy's mom drops her off at school at the beginning, watch closely when Buffy gets out of the car. In the passenger door's quarter glass window, you can see a reflection of a set-light (probably a fill light to eliminate shadows) for a few seconds when she opens the door.
Visible crew/equipment: In the beginning, when Buffy is having the prophetic dream, there's a shot right as it's about to end where the camera is above her and moving down closer to her. If you watch, you can blatantly see a shadow (more than likely the camera rig) grow over her as it gets closer and closer to her.
Plot hole: There was no need for the master wait 60 years for the night of the Harvest, when all he had to do was have his minions kidnap and gather a bunch of humans and bring them down to where he is so he could feed on them himself and escape 60 years earlier.