I listen a lot to my "instinct". If I get the sense right away that we are not going to get along, chances are there is a reason for that!
Not that I wouldn't go ahead based on a gut reaction, but it makes me think, for sure.
I watch how parents interact with thier kids, and whether they set boundaries, etc while they are here. Do they let them run around like a psycho and trash the place? If so, hmmm...I watch how the kids talk to their parents (if old enough) and how they respond back. That speaks volumes to me, as it shows whether there is a respectful relationship between them or not.
Agreed that if they have NO questions for you, sometimes that can be concerning. The "easiest" interview I ever had (no questions or concerns, I could kind of tell that they had made up thier minds before even coming over, to start care) turned out to be my worst family to date. They just didn't give a S#@*.....
If someone asks me all types of worst-case-scenario type questions, I would also be concerned. Again, not a deal breaker, but I don't like working with someone who is always looking for the negative in things.
I have not checked out any caregiver references yet, as I have mostly had kids who haven't really been in daycare yet. Also, I can see the benefit to it, but I think I would rather make up my own mind about people. Everyone deserves another chance, and if things aren't going to work out, I will find out soon enough. (Maybe that is a naive and silly thought?)