Captain Casey is based on real life impostor Fedinand Waldo Demara who managed to get a position as ship's surgeon aboard a Canadian war ship that was involved in the Korean War. As Dr. Joseph Cyr, Demara famously operated on 16 wounded Korean casualties that were brought aboard his ship.
Frank got his nickname "Ferret Face", not from Hawkeye, but from his brother as a child. He confesses this to Hawkeye after getting drunk on gin from the Swamp's still.
After "Captain Casey" confesses that he is not a doctor, or a captain for that matter, he tells Hawkeye that his actual name is Schwartz. This has a connection to the movie "The Great Impostor" because the real name of Tony Curtis, who played impostor Fernando Demara in the movie, was in fact Bernie Schwartz.
The diploma school Radar is using to get his HS diploma is the Triple-A High School Diploma Company of Delevan, Indiana. Gary Burghoff, who played Radar, lived in Delavan, Wisconsin in his youth.