Revealing mistake: As Willow is raising the satanic temple from the earth, we can see the support cables holding the temple upright from behind. This is plainly visible in the bottom right hand corner, complete with bright orange clasps on the temple itself.
Continuity mistake: During the opening of the season 6 episode "Grave," Willow's nose starts bleeding and she gets blood on her upper lip. Over the next several shots the blood consistently keeps appearing and disappearing.
Visible crew/equipment: When Xander is leaning over the hole in the cemetery into which Buffy and Dawn have fallen, he causes the edge of the hole to collapse. Seen from below, everything is fine, but the shot from above Xander shows a hand grabbing hold of the back of his trousers and his briefs are visible.
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 ★