I realize the temporality of the show is a mess (a comedy attempting to comment on Vietnam via Korea) - but, as I understand it, the show was very controversial, and I assume that would have put significant pressure on them to maintain some grounding in reality.
What did the show get right about Korea?
What did it get right about Vietnam?
The film and show are based on Richard Hooker's novel; "MASH: A Novel About Three Army Doctors".
"Richard Hooker" was a pseudonym for Dr. Richard Hornberger and writer Wilfred Charles Heinz who wrote the book as a collaborative. It was based on Hornberger's (Hooker's) experiences with the 8055th MASH unit during the Korean War. Hornberger had tried for 11 years to publish his novel before collaborating with W.C. Heinz on the book.
The subtext of the subsequent movie and sitcom was about Vietnam, but the show itself based on the book, was about the fictional 4077th MASH in Korea.
MASH as an overall (novel, movie, and sitcom) was received in a mostly positive way. The film was also deemed "culturally significant" by Congress and was selected for preservation within the National Film Registry.
Hooker (Hornberger) went on to write sequels of MASH.
The show took many liberties from the book, as they almost always tend to do. However, the portrayal of daily operations of a MASH unit in Korea was fairly accurate. The use of H-13C Sioux helicopters in the show is accurate, uniforms are fairly consistent with the period, weapons and materiel (much of the issued equipment during the Korean War was Second World War production), vehicles utilized are accurate, procedures are fairly accurate, even the premise of characters induction of mandatory service and their attitude towards such is relatively accurate.
While the subtext was about Vietnam, MASH is relatable to more than just Korea or Vietnam. The hardships, trials, and tribulations aren't solely unique to those conflicts, even today many of the moral, ethical, and other dilemmas visited in the show exist in similar military units deployed around the world.
What makes MASH a superb compilation of varying types of media and to a point "culturally significant"; is it shows the humanity and inhumanity of war, the insanity that exists in war, and the depth that the human mind will go to maintain sanity.