This report out of Atlanta is scary. They find thousands of people who are registered to vote in both Georgia and another state. And several people who have actually voted in more than one state.
One really key concern that this story suggests is the potential for fraud among college students. Because there is no law that requires you to unregister in one state if you register in another, it is very easy to register in a new state and still vote in your old state (leaving aside the ethics of college students voting in a state where they have no plan to establish permanent residency). I really hope that this is not a big problem, but I fear that this hope may be somewhat naive.