Throughout the episode, Loretta Swit's fingernails are over an inch long. No nurse, especially a head nurse, would have fingernails that long.
On the way to the 8063rd MASH, artillery shells rain down around the jeep in which Hawkeye and Margaret are driving. Even though the shells are exploding as close as 5, 6 yards away (well in their kill range) the blasts never knock the jeep over and neither Margaret nor Hawkeye are hit by any shrapnel (a feat any combat veteran would envy, particularly those with Purple Hearts).
When Hawkeye and Margaret leave the abandoned MASH unit, you can see the tire tracks where the turn has been made several times before.
The Korean patrol uses M71 Valmet Sporter rifles, a license-made copy of the AK series, with synthetic stock and muzzle brake removed to be a stand in for AK-47s. This is inaccurate because even the Soviet Union and China didn't issue AKs for several years after the end of the Korean War.
After shelling begins again, Hawkeye lights a candle. This makes him an easier target.
When Hawkeye and Margaret were taking cover in the abandoned hut, Hawkeye claimed he had "Japanese Scotch". There is no such thing. All scotch is by definition a whiskey made in Scotland using traditional Scottish distilling techniques. Anything made in Japan would simply be whiskey.
Margret describes her last letter from Donald of how it dealt entirely with self-loading semi-automatic sub-machine gun. Submachine guns are NOT semi-automatic, they are fully automatic. Semi-automatic weapons need to have the trigger pulled each time to fire each round (in other words, they fire only once when the trigger is pulled). Fully automatic weapons keep firing as long as the trigger is kept pulled and only stop firing when the trigger is released. Continuous (automatic) fire is what makes a sub-machine gun a machine gun. Margaret, an Army brat and Army career woman, would know all of this and therefore would NEVER have made such mistake.