My grandparents owned several rental properties throughout the years, and my brother had one for a while. Nuggets of info I've taken from watching:
1. Require them to purchase rental insurance, and they have to show you proof.
2. Get more than one reference. Their current landlord may give them a good reference just to get them out of his/her hair.
3. I believe Clark Howard has some landlord tips on his website somewhere. I remember him saying he offered a discount of $50 or some such thing if they paid the rent before the 1st of the month - he's never had a late payment.
ETA: Here's a link to Clark's website. He did a series of articles about renters, this is only one of them, so you might want to did for the rest.
http://www.clarkhoward.com/news/clar...-tenant/nYRL3/