Pan Am captains did not look like teenagers.
It's been years since I've seen this movie, but I seem to recall a scene where DiCaprio approaches a ticket counter, dressed as a Pan Am captain, to get a ticket or boarding pass to fly "dead-head" as a passenger.
My father was a Pan Am captain, and Pan Am (and most or all U.S. airlines) promoted strictly on a seniority system. Depending on whether they were hired before or during the huge post-WWII influx of pilots from the ranks of discharged military flyers, pilots were lucky to attain captain rank by their late forties. (Mandatory retirement age was age 60.) No matter how great pilots might have been, they were rigidly locked-in by their seniority-list, and could only be promoted from first officer to captain as fast as the man in front of him on the list.
If someone as young-looking as DiCaprio had approached a ticket counter (even a different airline's) posing as a Pan Am captain, he'd have been spotted as a fraud immediately, and the police would have been called. Even if he had been passed through by a brand new counter agent, there is no airline pilot on the planet that would have failed to spot the fraud and call it in before take-off.