Very difficult decision I agree but I think it was elementary school that I started to allow 2-hour playdates with families that I was unfamiliar with but... the first playdate was ALWAYS at my house. When they are first asked, I come straight out and tell the parents that I would love to meet mom or dad and would like them to bring the child to play at my house where I serve a light snack like coffee/pastry, or lemonade/pie sort of thing. I fully expect the parents to stay the entire time if they'd like but I do expect them to stay for an hour or so to "chat em up" and they can do likewise to me
I expect that when my DD10 (the other is nearly 18) goes to a new home that they may have very different rules than what I have. DD knows MY rules and knows to call me if she isn't sure if something would be okay with me. The one and only time this was a problem I think she was 7 or 8 and I picked her up at a new friends' home. After meeting mom and having a playdate at our house, I knew this friendship was going to present some issues. The family (mom and 2 kids just like me) had little money, lived in low-income housing, and were not very clean but I of course let DD go because those are just not reasons I would decline a playdate for. When I picked her up she was painted up like a two-bit well you know

, was absolutely filthy and covered with dog hair and was playing in a yard that was filled with animal poop! Yuck! Mom said "don't worry, she's had dinner -- they made their own hot dogs and fries" -- good going Mom, DD doesn't know how to cook, lol.
Anyways, family has moved away and that's that but back to the question... I think you have to trust your children to call you when they feel uncomfortable. I always tell the parents to please allow DD to use the phone if she asks to call me (so there's never a misunderstanding on this). DD has many friends that actually have their own cell phones at this age and are constantly in touch with their parents when they are here.
As for sleepovers, whole nother discussion -- I am extremely paranoid about letting DD sleep anywhere that I am not really familiar with everyone in the house, including boyfriends and girlfriends of teens, etc. I wasn't this bad with DS but I just think a little girl has more of a chance of running into trouble with the drunk uncle or boyfriend or other males. I also have an issue with her driving with others after dinner because I'm afraid that someone driving might have been drinking.