Obviously the show is fictional and the unit is unique in it's dysfunctionality.
My question is, is it true to real life? Were Army doctors (the doctors in mash are draftees) given some leeway in terms of military discipline?
Enlistees in the U.S. Army who already have a medical degree (MD or DO) are automatically commissioned officers, usually with the rank of Captain. Physicians do not have to attend basic training or officer candidate school, unlike most other military personnel. Unlike many other officers (especially careerists), physicians in the U.S. military usually have substantial life experience outside of the military, which colors their approach to military life.
The U.S. Military has historically struggled to retain skilled medical personnel and therefore was disinclined to subject them to some of the harsher forms of military discipline, since physicians require many more years of training and education (usually outside of the military) than most other types of specialists, and have many job opportunities outside of military.