The documents, revealing details not previously made public, were filed in federal district court in Manhattan by lawyers on behalf of the family of Mark Bavis, who was on United Flight 175 that crashed into the World Trade Centre.
The lawsuit is the only remaining wrongful-death lawsuit out of the 100 filed after the attacks.
The case against United and security firm Huntleigh USA will go on trial in November.
"This document demonstrates that 9/11 was completely preventable at the checkpoint for this flight, and that United did not live up to its responsibilities for security," Donald Migliori, a lawyer for the family, said in a New York Times report.
The lawsuit contends that United's checkpoint at Boston's Logan International Airport, from where the terrorists boarded Flight 175, was manned by a staff that did not have the necessary training or the experience to do their jobs.
Some screeners' training records showed that they could not read airline tickets and marking labels, while one supervisor on duty was a 19-year-old employee who had just about three months of experience, the lawyers said.
"Many of United and Huntleigh's security screeners on duty on 9/11 were unable to speak or understand English," the lawyers said in the lawsuit.
"One pre-board screener had such a poor grasp of the English language that she required an interpreter during her deposition," they added.
Citing testimony given at the time of deposition by the screeners, the lawsuit said at least nine screeners on duty on September 11 had never heard of bin Laden or al Qaeda.
The hijackers had used knives, Mace and had threatened that a bomb would go off to take control of the flight.
The lawsuit alleges that due to the lack of proper training, the screeners and staff at the checkpoint could not even identify the Mace that the terrorists had carried in their bags, thereby failing to prevent the hijackers from carrying it onboard the plane.
"Four screeners working the Flight 175 checkpoint did not even know what Mace was," the lawyers said.
"One of the screeners was still unable to identify Mace when handed the Mace canister".