There are probably more people like NSA leaker Edward Snowden working right now with America's secrets says a former deputy secretary of Defense. John Hamre tells Scott Pelley that the U.S. security clearance process -- the one that green-lit Snowden as well as convicted spy Chelsea Manning and mass murderer Aaron Alexis -- is obsolete. In fact, an internal government memo obtained by 60 Minutes warns the process could contain "systemic problems." Pelley's report, "Into Dangerous Hands," will be broadcast on 60 Minutes Sunday, Nov. 8 at 7:30 p.m. ET and 7 p.m. PT.

"We have spies in our midst. I'm convinced of it," says Hamre, who also chairs the Defense Policy Board, which advises the Pentagon. "Our system is very obsolete in my view."

Its basic flaw is a form applicants fill out themselves on which people can lie and not get caught. Alexis, who killed 12 coworkers at a U.S. Naval office, lied about a felony arrest for letting the air out of someone's tire. He failed to mention he did it with a gun in a "black out fueled by anger." Snowden worked for the CIA and left there under a cloud that convinced the agency to put a red flag in his file. But when his security clearance was later reviewed, after he took a contract position with the NSA, he said his past employment was "classified" and the clearance investigator did not check with the CIA.

Hamre says this kind of lapse is an example of the most serious threats the system faces. "Snowden was an example of it. He moved into an enormously sensitive position," says Hamre. "We control people at the gate and once we give them a credential, they're in the compound, we don't pay attention to where they are after that...So our big elaborate, expensive system didn't prevent something that was truly important."

Responsibility for most government security clearance investigations falls under the Office of Personnel Management, or OPM. 60 Minutes obtained a memo written by the OPM's Inspector General Patrick McFarland in the wake of Snowden's disclosures of classified NSA documents to journalists. McFarland writes that Snowden's background investigation was "...deficient in a number of areas..." and "...OPM itself did not identify that the report had glaring deficiencies." McFarland concludes, "there may well be systemic problems."

Manning lied on his application about his mental health history. Hamre points out that authorities are not even permitted to search applicants' social media accounts because of privacy concerns. "It's amazing what people will say on their Facebook account that they don't say on a security clearance," Hamre tells Pelley.

Representatives of the OPM declined to be interviewed for this report, but told 60 Minutes in a statement that they are "working aggressively to incorporate new data sources and to transform investigation methods" and that they are "...currently reviewing key aspects of the security clearance process."