Among the things already listed, I'd also ask for a list of references (preferrably at least 5 or more referrences) and I'd check on them and ask them their opinions (pros and cons according to their experiences). I'd also see about doing a background check on them as well as anyone who regularly visits their home. I'd also be sure to observe the other children's interacations with and demeanor toward them... perhaps requesting that you are allowed to give a "trial run" by staying and getting to know them and your child/ren getting to know them for a couple of hours on a given day (prescheduled) ..so then you can get a good "feel" for things. If you feel uneasy, that would be a red flag that this isn't a good/safe place for your child/ren.
at 1:56 PM on Nov. 13, 2010