Continuity mistake: In the basement scene, with Jack and Xander, the bomb counts down from 13 to 10 seconds. Then after Xander says his line, the bomb again shows 13 seconds.
Continuity mistake: In the school near the end, one of the dead guys looks through the round window into the library and says 'wow'. In the long shot from within the library, his face isn't in the window. Back to the shot of the window, he's still there.
Continuity mistake: When Xander's being threatened, the knife moves from under his chin to the side of his neck between shots.
Visible crew/equipment: While Buffy, Giles, and the gang are in the library fighting the demon that came out of the Hellmouth, the camera zooms toward the door that leads into the hall, where you can see Xander being chased by the dead guys. As the camera zooms in closer towards the round window in the door, you can see its reflection in the glass when the strobe light flashes. (00:36:10)
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 ★