Most people are surprised to discover that voter registration rolls are run exclusively by local election authorities, who are usually somewhat obscure elected officials, instead of by a statewide or national organization.
There is no national database of voters.
So when people register to vote in two states, there is simply no way to catch that.
Similarly, the statewide databases where at least the government can discover whether someone is registered in two different places in the same state are slow in coming, even though there's a 1/1/2006 deadline under federal law to have them up and running, and most election authorities fight hard to keep them locally-controlled instead of state-controlled.
This Tribune article details how tens of thousands of bad names (dead people, etc.) routinely stay on voter registration rolls.
What should happen is that the government, and not the citizen, should have the responsibility to create an accurate voter registration roll. Now, the citizen must affirmatively contact the government and ask to be registered. Most democracies don't do it that way -- the government has the responsibility to ensure that all citizens are on the rolls. Because the government is essentially passive in the creation of voter registration rolls (that is, waiting for citizens to contact them), lots of omissions happen.
Add on to that the 2-week or 4-week period before elections when it is illegal to register to vote, and we have an institutional bias against participation, especially for first-time voters.
Think of all the government databases on citizens -- post office change of address forms, tax records, employment records, drivers license records, public assistance, etc. Only a few of those are somewhat coordinated with local election officials voter registration databases -- and that happens only if the citizen requests that the information be shared. It doesn't happen automatically.
When you change your mailing address with the Post Office, your voter registration should also be changed automatically.
When young men register for the draft (and they still have to do that), they should be automatically registered to vote.
When a student enrolls in a public high school or public college (or private college, for that matter), the student should be automatically registered to vote.
That's the direction we should move, and again, Blue America states and localities will show the way, since our Red Congress is unlikely to care much about increasing voter registration.