In my years as a Mortgage Broker, I have heard many unsavoury stories about renting a property to the wrong tenant. I also know quite a few property investors that have used rental properties to fund a comfortable retirement and swear by it. I often ask them what they watch out for and they often say that they try to visit the tenant at their current home to see the way they live. I think the above would probably tell you everything you want to know about your possible tenant.
Here's a really good article about how to avoid the wrong tenant!
Article: How landlords can steer clear of bad tenants