"We were walking to the plane on the runway," he said. "And while we were walking a gentleman next to me turned to the pilot and said 'I'm carrying.' I kind of deduced, you know, that he has a gun."
Valenti said the passenger voluntarily turned the gun over to the pilot, who kept it in the cockpit during the flight. But Valenti said the passenger could have easily kept the gun on the flight.
"At that point, I started to have some serious questions about the safety on these flights," he said. "No one was checking for guns. No one asked anyone if they had a gun."
JetSmarter refused to comment on the incident.
The security issues at JetSmarter are likely to become more common throughout the industry, as more and more jet companies offer passengers the chance to book individual seats on private jet flights. The current security procedures for private jet flights and terminals were created for mainly jets that were flying a single family or executives from the same company. Now, passengers are able to book an individual seat on a plane – much like a commercial flight, but without the same level of security. What's more, cockpit doors on many private jets are not armed, and many cockpits are open throughout the flights.
The Transportation Security Administration requires passengers to be positively identified before boarding a private jet and to be screened for the TSA No-Fly List. The same items banned on commercial flights – everything from weapons to narcotics to large liquids --- are also prohibited on private jets. But there is often no physical screening of bags or passengers.
"It's a huge loophole," said one pilot who flew JetSmarter flights. "On many of their flights there is basically zero security."
Sally Horchow, another JetSmarter member, said she talked to other passengers who appeared to choose to fly JetSmarter specifically because of the more relaxed security compared with commercial flights.
"I met one person on an earlier flight who, while I didn't actually see the bag full of cash, he kind of motioned to it," Horchow said. "He explained to me that one of the reasons he had signed up for JetSmarter was that he had been detained at JFK after getting off a commercial flight with a bag of pot-smelling cash, and that was a real hassle for him. So he was really happy to have this option."
One flight attendant said she witnessed passengers doing cocaine on a flight. Another said she was once offered drugs as a gratuity.
Valenti said he met passengers who told him they were in the marijuana business.
"When I would talk to people on the flights occasionally, they would tell me that's what they do, they move weed between states where it's legal to have it and illegal to have it. And they were able to use JetSmarter as a big part of their business."
— CNBC's Bianca Fortis contributed to this report.