Pernell Roberts publicly denounced series television when he left Bonanza (1959) for theatre in 1965. He decided to return to television because his salary would help support his aging father. He also felt that he would be able to exercise his acting range and address social issues, two things he felt he was rarely able to do on Bonanza.
The first couple minutes of the pilot is the only time when they attempt to tie this to the MASH franchise. Trapper is asleep, and you see pictures of the 4077th scattered around his room. He says, "Hawkeye? Are you there?" The rest of the time this show is a standalone series with no other references to the franchise whatsoever.
Wayne Rogers, who played Trapper John in M*A*S*H (1972), turned down the role because he did not want to play a doctor again on television. (He later played a doctor on the television show House Calls (1979), itself a spinoff of a movie, House Calls (1978).)
Richard Hornberger was a gifted surgeon whose memoire of his experiences, MASH: A Novel of Three Army Doctors, became the basis for the hit 1970 Robert Altman film as well as the hit television series bearing the same name. Trapper John was one of the lead characters in the movie and TV show. Since then, numerous articles and the 2010 documentary "The Real MASH" revealed that Trapper, Hawkeye, Margaret, and others were based on real people. Trapper John McIntrye, Hawkeye's wingman, was based on another doctor that served in the 8055th with Hoernberger and befriended him. Dr. James Dickson was a young doctor from Ohio who was friends with Hoernberger and was the prototype for Trapper John, M.D.
When Mary McCarty died during the hiatus between the first and second seasons, her absence was explained by having her character get married and move away.