When Mack is captured and interrogated by the Major, the Major demands Mack's serial number. Mack responds with a number beginning with "RA" meaning "Regular Army". The US Army transitioned from serial numbers to social security numbers in 1969. Neither the Major nor Mack would have been old enough to have been issued an RA serial number.
When the Major's assistance first encounters Mack, he sees the 101st Airborne Divison tattoo on his chest and he says "Paratrooper, huh?" While they are still called the 101st Airborne Division, they for the most part Air Assault, not Airborne...not Paratroopers. AATW.