My son is allowed to play at the homes of neighbors unsupervised for short periods of time (one hour). Its not really much different than babysitting IMHO for *us*. We live in a very close knit neighborhood with all SAHM's and small toddlers, babies, preschoolers. They all play together on a daily basis outside or at each others homes and we all know the "quirks" of each others children (who is bossy, who is sensitive, who does what, etc etc) and the children are all very comfortable with the adults as well. We are in each others homes so frequently our children know where we keep each others snacks LOL
I have left my son with the same neighbors for dr. appts so to me it is the same thing. As long as they play inside. I don't have the same level of trust for outside play, nobody has fenced yards but ME.
I have not/do not plan on leaving him with any of my "acquaintances" - gals from playgroup or met on playground who you meet for park dates whatever. Just my neighbors.
HTH Oh, BTW, my son is almost 3.