Deliberate mistake: While it is established that Angel doesn't age, it's obvious across both Buffy and Angel that David Boreanaz gets older. More unavoidable than deliberate, but still worth noting.
Deliberate mistake: Though vampires are said to possess super-human strength, and are in fact demonstrated to have it, they are often kept confined by the flimsiest of restraints. One distinct example is in season 2 episode 9 when Kendra locks up Angel he is unable to break out despite being held in by nothing but a flimsy padlock. This mistake is pointed out in the DVD commentary as an unavoidable 'mistake'.
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 ★