Continuity mistake: In the library, a book in front of Buffy begins to slide off of a stack of books. Change of camera and book is back on top of stack.
Visible crew/equipment: Near the start, just after Buffy kicks the vampire onto the roundabout, check the top left corner of the screen as she says her line - boom in shot. (00:02:35)
Plot hole: When Buffy enters the house to rescue her mother she uses a stake to stop the front door from closing. A vampire then grabs it and the door closes. Why did Buffy use a stake knowing that there was a vampire there when she was almost killed by a vampire with her own stake earlier in the episode because Giles had been injecting her with a muscle relaxant?
Chosen answer: From what we see in the series, certain girls are identifiable as potential Slayers - Kendra clearly fell into this category. The identification method is presumably mystical in nature, but the Watchers' Council are pretty effective at that sort of thing, so they're quite good at tracking down the potentials ahead of time. Not perfect, though - it does appear that Buffy herself may have slipped through the net - certainly she had no inkling of what she was until she'd already taken on the role of Slayer. It is possible, however, that this was actually cultural - an American family would hardly be likely to turn over their daughter to some strange man for 'training', so the Watchers might have chosen to keep an eye on her covertly, whereas some other cultures (like Kendra's Jamaican parents) might be more willing to believe.
Tailkinker ★