@Warren208
Airbnb guests are one thing and tenants are another. With tenants, of course you can do credit and background checks if you choose and I would definitely ask for previous landlord references. When I used to have lodgers, I would ask for employment details and personal referees, then email or call them as well as the landlords. They would also need to sign a contract (which included a list of house rules) and pay a deposit.
However, with Airbnb it is different. I am assuming you are planning on using it for long term stays? If not, I really think it would be difficult for you to do most of those things and, even for longer stays, it's not easy. There is certainly very little you can do before the booking is made, as you are not allowed to exchange contact details with the guest, and after that, there are penalties if you cancel (although you can cancel instant bookings penalty free 3 x a year under certain circumstances).
Personally, I require guests to have their ID verified by Airbnb and to have uploaded a profile photo. They need to tell me a bit about themselves and confirm they have read the full listing and house rules (I have a question in there that they have to answer so I know they have done this).
Also, look at the guest's reviews and ratings. If you see anything problematic there, then that would be the point at which you might contact a previous host to ask about it. I don't see the point in contacting hosts that have left the guest a great review. That is what the review system is for. I also check the reviews the guest has left for previous hosts as sometimes you can spot red flags there.
Of course, you will get requests from guests who don't have any reviews yet. In those circumstances, communication with the guest is even more important.
I know it's not a lot to go on, and Airbnb doesn't even collect a security deposit, so some hosts do ask to see the guest's ID or ask for a deposit of some sort.