Had one for DD's (4.5 yo) party last summer, was a bunch of fun, and no mishaps involving guests. We had plenty of parents in attendence (in the bounce house, even) so supervision wasn't an issue. I wouldn't have been comfortable if it had been a drop-off party, though.
One thing did happen that I hadn't considered in advance -- the electrical load from the fan that keeps the house inflated overloded a circuit (or something). The power to the fan shut off, and the bounce house began to collapse -- on DD, who was trying it out in advance of the party.
When I heard the fan stop, I think I broke a land speed record getting from the kitchen to the bounce house to pull DD out. [cringe, see above, supervision.] I know that the company that I rented from would also rent a generator to power the fan; I opted out of that because of the noise and the exhaust and the whole set up was at grandma's house, with lots of outside sockets, so no problem in just plugging in the fan. Eh. Not so much. I don't know that there's any way to figure out whether this would happen in your setting, but I offer my experience FWIW. If we do this again at G-ma's, I might have an electrician in to look at her breaker box in advance.