Director Robert Altman's 14-year-old son, Mike, wrote the lyrics to the MASH theme "Suicide Is Painless," and in the end received more money in royalties than his father did for directing it. http://www.absoluteastronomy.com/encyclopedia/m/mi/mike_altman.htm See more...
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Revealing: Near the end of the film, there is a football game played between the rival MASH units. Although the game is supposed to be taking place in a remote location of Korea in 1951, late model 1960's automobiles can be seen driving on a nearby highway as the game progresses. This gave away the fact that the football scenes were shot at a university in Southern California.
Factual error: When Hawkeye and Trapper arrive in Japan, as they approach the hospital in a Jeep, you can see a football field in the background. Look closely at the goalpost on the field. Instead of looking like an "H" (then in use), it is in the style used since the late 1960s: a bent single goalpost, a crossbar, and the uprights.