Okay, I know people have said it before numerous times around the forums, but for my sake and for the sake of all the other newbies...
What evidence should I have, besides a false alibi, before I accuse a suspect?
Definitely right about the alibi. I had an unusual number of suspects that clammed after they had given me an alibi thus increasing the probability that the one WE I had was the mislead.
Usually you can get away with it although I have had one case where two suspects with False alibis pointed at each other and went "It was him" (This caused much grinding of teeth)