A: That's a really great question! I think you should ask for a reference--that is, a previous parent that the sitter has worked for. Explore with the other parents how many times the sitter actually sat for their children and whether there were any questions about the sitter's reliability or judgment. If there are no previous parents who can report upon their experiences, ask for some other adult reference who knows the sitter well. You want to know that a disinterested third-party can actually document that your potential sitter is a completely trustworthy person. Finding out from someone other than the sitter what kind of person the sitter really is--this is more important than asking questions of the sitter, because many people whom you would not want to sit for your offspring may nevertheless be skilled at presenting themselves in a positive light. The sitter could be a dishonest person, and many dishonest people are very clever and charming. Beware!
It would also be good to ask the sitter directly "What would you do if the child starts to choke?" or "What would you do if you see flames and smoke coming out of the air vent?" or other emergencies. Spend some time getting to know the sitter. If you don't like the vibes, don't hire them. Trust your gut.