I just had a conversation with an old friend from college that had an unfortunate experience with an AirBnb in Italy. It was on AirBnb, but apparently wasn't properly registered and lost the booking the day before arrival.
Very many cities now require short term rentals to registered or licensed. Almost always when this is a requirement the registration number must be in the advertising. I really do believe that AirBnb does try and weed out the non-compliant units but they dont get them all. I think this one WAS caught by AirBnb and thats why the reservation went up in smoke.
I spoke to a RS person a few months back and warned him the unit he was about to rent was not legal. He communicated with the host and determined that indeed it was not licensed .... but rented anyway. Short Term Rentals get a lot of bad press as it is so lets not support the law breakers. That just leads to more restrictions.
I couldn't find a comprehensive list of the cities that require licenses and registration numbers, but its not that hard to guess. Go to a city on AirBnb, Budapest for instance, and look and see if listings have a registration number. If you see twenty listings with numbers and two listings without, thats a giveaway. Or ask on the RS forum, I suspect we have a local in most large tourist destinations.
Renting within a platform like AirBnb, VRBO or Booking.com will increase the likelihood that its legal as well, as they do try and weed out the ones that are not conforming, where an individual website has no policing.