Continuity mistake: There are two sets of the 4077 compound - the outside Fox Ranch set located at Malibu Creek State Park, and the second set inside the studio's Stage 9. The layout of both sets are quite different - Studio 9's set was vastly smaller than the Ranch set, so things such as the proximity of the Swamp to the mess tent are different between the shots filmed at the Ranch and shots filmed at Studio 9, when seen within the very same episodes.
Deliberate mistake: These errors I assume were caused by the show running 3 times longer than the real war. Col. Potter arrived at MASH in September 1952 a year before the war ended, then a few months passed by Margaret got engaged for 8 months, then Frank Burns left and Charles took his place. In this time the war would have ended. In the final episode Margaret mentions Charles has been there for 2 years. Which means he would have arrived in 1951 a year before Trapper and Henry left and Col. Potter arrived. It's a lot to take in.
Other mistake: Across the show, several times doctors looking at an x-ray picture say things like, "Looks like he swallowed a whole junkyard" or "His belly is full of shrapnel." In fact, shrapnel, being metal fragments, should show up as clear white spots on the x-ray pictures, but none of that is visible in any of the x-rays shown throughout the show.
Continuity mistake: In any scenes in the CO's office, look at the windows - they're sometimes opaque, sometimes clear. Also the windows in the OR. Usually semi-opaque, once, they were totally opaque, and made of a thick plastic. This was because it was very cold outside, and Hawkeye used a scalpel to cut them open to let in cooler air.
Revealing mistake: A number of times, during the night periods (for instance, during an OR scene) the windows are dark when the lights are on in the room. Then when the lights go out, the windows brighten up. They, and the interior lights seem to alternate lightening and darkening.
Other mistake: Many times during the series, soldiers are around the OR carrying a loaded weapon (magazine attached for example), when there is a sign outside the entrance that says "all weapons must be cleared before entering the building" or similar.
Other mistake: In all the opening sequence of each episode, a group of people are waiting on the pad to get the wounded off the choppers. If you look closely as the group goes to move, Mulcahy is there, but it's George Morgan, who played the role in the pilot episode. From the third episode on, it was played by William Christopher.