In an earlier episode, it was mentioned that Don had attended night school. Sounds like he might have dipped into the GI Bill on that one. Don is not exactly a big rule follower, so I do not know why you would believe him scamming the VA would be above him.

The finger print card from his military induction would take some real digging to find back in those days. Maybe not impossible, but the search would only occur if they were in fact trying to prove he had made the identity switch.

Back in 1963, Dick/Don would have had difficulty finding a "good" lawyer to take his case. His would have been a very unpopular case, especially in the months following the death of a war hero President. The New York Daily News would have torn Dick/Don apart. He would have been convicted in the press, long before he went to trial.

Do you really believe the Conservative Texan Hilton, or Navy man Roger Sterling would stand by this deserter. Also, the Manchurian candidate came out about that time. The movie got buried because of the Kennedy assasination, but the story line indicates how suspect a deserter of that conflict who assumed an officer's identity would be. People might even suspect he had a hand in the death of the real Cpt Draper. Hell, If MM had not actually shown the sequence of how Cpt Drapper was killed, I might suspect it myself.

Dick/Don would run. Nothing in his character indicates he would face the music.