Other mistake: The newspaper that Xander is reading in the library has the same text over and over again and does not at all match the headlines. (00:18:05)
Other mistake: As Spike follows Buffy into the hallway by her front door we see Spike's reflection in the mirror. Vampires do not have reflections, so Spike should not have been visible.
Seeing Red - S6-E19
Other mistake: At the Bronze, when Warren punches Xander the first time, Warren never actually punches him, and Xander starts to go up in the air before you even hear the sound of the punch.
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 ★