Continuity mistake: During the inspection of arms, when Frank stands in front of the second soldier in line, the soldier's left collar is flipped up and his right collar is folded underneath his shirt in the shots facing him, but in shots facing Frank the soldier's entire collar is properly positioned.
Factual error: When Frank sits down on Margaret's bed, he pulls a single metal star out of his butt. Kelly being a Lt. Gen, he should have (and has, as can be seen in other scenes) a single bar of three interconnected stars, not three single ones. Therefore Frank shouldn't be able to find a solitary star in Margaret's bed. (00:19:00)
Continuity mistake: After Iron Guts Kelly dies in Margaret's tent, Frank Burns visits Margaret, suspecting something. Frank asks why there is a general's star on her cot. In the ensuing 'back and forth' dialogue, Margaret's hair goes (in close ups) from nicely combed, to frazzled, back to nicely combed again (and in a different light).
Revealing mistake: As Hawkeye calls for quiet in the officers' club, Henry pulls the tonearm off the record player, it comes away trailing a long wire behind it. Why would it even have a long wire to trail? After all, wire costs money too. It's not like the tonearm is designed to come off and be used remotely. My guess is: they lengthened it, so the shot could be taken several times without repairing the record player every time. Now, WHY they would do it that way and not simply use a dud record player is beyond me. (00:20:55)