Contact any previous tenants and ask why they moved out. Ask your potential landlord if you can put a lock on the door. If your landlord is close to a university or college, call the housing office to see if there have been any complaints from students.
Some universities have a rating system for landlords.
Pay close attention to how they handle their accounts and check for public records which may indicate an action against them by a landlord. Call all references. Call previous landlords. Call present employer to verify income. Roommate Locator Inc.