You can ask the previous landlord about their character, housekeeping, rent history, would they rent to them again? Be careful about the "Fair Housing Laws". There are certain questions that you cannot ask such as race, religion, sex, disability, number of children (this is where the applications comes in handy, because you'll see the age of everyone). Check with your local and state government regarding the Fair Housing Act. I have the applicant to complete an application in which I do a credit check, criminal background, as well as previous evictions, which is public record. You can't rely on the previous landlord. What if it's a bad tenant? They'll say anything just to get rid of them. So do a background check (notice I said background, not credit check). You can find a service in your area that will do it for you. Pass the charge on to the applicant as a nonrefundable background check fee. When you collect the fee, tell the applicant exactly what it's for. Advise them them that you will be checking credit, criminal, and evictions. This way, they won't waste their money if something comes up on their criminal and previous rental history (evictions). Previous evictions and felons are an automatic rejection for me. If they didn't treat their previous landlord fair, why would they be different towards you?
Nothing is full proof, but you have the right to know what you're getting into when you rent out your unit.
School of "Hard Knocks"