Continuity mistake: When the detective is interviewing the woman in the alley, he mentions that the murder took place "last night". In "Bad Girls", we see Buffy visiting Faith the day after the murder, and that night is presumably when she has the dream about drowning, so by the time the detective is asking this question it is actually two nights after the murder, not one.
Other mistake: When the detective is interviewing the woman in the alley he says "So you heard the man scream about what time?", but Finch didn't scream as he died.
Continuity mistake: In 'Consequences' Buffy says to Faith 'Less that 24 hours ago you killed a man'. In 'Bad Girls', Faith kills Finch in the alley on the first night. One night later Buffy and Angel are attacking Belthazor, the night after that is the night when Buffy dreams about drowning, so the night when Buffy says this is actually about 72 hours after the murder. (00:11:25)
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 ★