If your babysitter was a mean person, would you want to know?
I don't mean that she's mean to your child, but rather mean to other people--other babysitters, parents, and other kids? I saw a woman on the street this morning and physically shrank back, then realized that she's the babysitter of a kid when ran into sometimes at the playground, and that she'd been nasty to me and said some pretty vicious things about my older son to the child she cares for.
I think this is an interesting question, because it has so many dimensions. On the one hand, unless you're a clergyperson, I don't think there should be any kind of morals clause attached to employment. I don't care from an employer's perspective about what my babysitter does when she's not with my kids. (My babysitter and I were friends before she started caring for my kids, though, so I do care about what she does personally, so I may not be the best test care here.)
But, if the babysitter is with your child all day, she's modeling social behavior. And being nasty to other people is not something you want modeled to your child day in and day out.
Plus, no one will want to play with your child if they know they're in firing range of the babysitter. (Eventually we stopped going to playgrounds we knew she frequented, because I didn't want my child insulted just because he wouldn't hand over one of his toys when the other child demanded it.) So your kid's going to end up with fewer other kids to play with, even if your child is absolutely delightful.
Opinions? Or maybe I'm the only one who finds this an interesting topic. Remember that this isn't something that would directly harm your child, or some behavior that's risky. Just nastiness.