The actual # of unemployed is most likely higher than the reported #s. They stop counting a person as unemployed after they stop receiving the unemployment checks, no matter if they found a job or ran out of time
http://www.bls.gov/cps/uiclaims.htm
Those numbers also probably understate the problem, but not for the reason you mentioned; the official unemployment numbers do not include people that are underemployed or those that have stopped actively looking for a job.