Continuity mistake: In the scene where Buffy and Kathy are deliberately infuriating each other (tapping pencils and cracking eggs) there are several lights on throughout the room (on Buffy's desk, above Kathy's computer, in the kitchenette) yet when Buffy turns out her bedside lamp, the entire area is thrown into darkness.
Continuity mistake: When the portal is opened Buffy crawls around to the other side of her bed yet just as the portal closes there is a wide shot and she isn't next to the bed.
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 ★