Everyone except the Department of Homeland Security (the US Congress apparently mandated a biometric exit logging system over a decade ago) seems to agree that a biometric check in/check out system is the way to go, but according to:
U.S. Struggles to Nab Visitors Who Overstay (Yahoo)
The department is no longer focused on implementing a biometric system, one relying on fingerprints or other unique personal markers, to make sure someone leaving the country is the same person who entered on a particular visa. Instead, the department has begun comparing lists of people with expired visas with lists of foreigners who depart through airports and seaports.
In order to be appropriately bewildered, one really must read the article in its entirety. For example: Among the reasons cited by the Secretary on behalf of the famously frugal DHS is that a biometric system would be “extraordinarily expensive.”