Barring a real-time clearance system (as I believe most stores still accepting checks tend to use), a check is just basically an IOU with a promise that there's enough money in your banking account to cover it. Especially in a rental situation, I'm not sure that the lack of an address is a huge red flag--after all, the person is probably between addresses. But a complete blank check without even a name on it? Yeah, that's a red flag given that, even if you've just opened up a new account, today you can get personalized checks within a few days if not on the spot.
