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.
Other mistake: During the surgery, after Hawkeye and Margaret reach the 8063rd, Margaret is explaining the procedure. She says that they are using a new vascular clamp designed at the 4077th. It appears that this is the clamp designed and built three episodes later in episode 16 "Patient 4077."
Continuity mistake: In the shot where Hawkeye presents the Spam lamb to Henry, he sets it down, and Henry asks him what it is. Behind Henry, you can see Hawkeye's shadow - and see his lips mouth the word "A Spam lamb". The camera then changes to a close-up of Hawkeye, saying "A Spam lamb".
Continuity mistake: In the mess tent, Hawkeye is attempting to get the reporter to focus on BJ instead of him by telling the guy about the defibrillator made by BJ to save a life in the O.R. As Hawkeye is making his point, the reporter is putting a sheet of paper into a folder on his typewriter case. After the camera cuts to a close up of the reporter saying his next line, he's putting the paper into the folder again.
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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.
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Revealing mistake: When Radar salutes Major Burns dropping the package, you can see wet spots on his uniform where he held the package. Before the bottle inside breaks, it is supposed to be dry. The crew probably re-used a single package for several takes of the shot.
Character mistake: When Hawkeye asks Frank what he is doing, Frank replies he is lining up all bottles and jars "according to height and popularity". In fact, the bottles are not lined up according to height at all, also the order of condiments is different on the two tables. The sweet and sour gherkins Frank mentions are not there at all - during the pan shots you can see the line ends with the pepper.
Factual error: Charles mistakenly injects a post op patient with curare instead of morphine. This would have been hard to do. Curare was not approved for use in Korea by the U.S. Army and it would not have been there. Even if it had been, curare was used in conjunction with anesthetics in the operating theatre. It would make no sense to have it in the post op. (source pg. 14 "Notable Names in Anasthesia" by J. Roger Maltby, Royal Society of Medicine - Great Britain).
Continuity mistake: In the assembly called by Major Burns at the beginning of the show, Klinger is in the front rank far left (except when the continuity error has him centre rear), but after the appearance of Hawkeye in the rickshaw Klinger isn't on parade at all.
Continuity mistake: After Klinger's file cabinet gets bombed, BJ appears in the window. He's facing directly ahead, head slightly tilted to the right. When the camera goes to a close up, he's in quarter profile, left cheek forward. In the long shot, he's back to the original position.
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Continuity mistake: When Hawkeye gets into the chow line and Igor suggests the peas and carrots, Hawkeye asks about the beans. As the peas and carrots are being scooped to be served to Hawkeye, he grabs Igor's arm and peas and carrots are spilled into the beans. Peas are VERY visible in the beans. The next shot with the beans, the peas and carrots have been removed from the beans.
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Plot hole: In a tape home, Winchester implores his father to get him out of the MASH and suggests that Senator Griswold should help as his father "paid good money for him". As the length of time the show ran so exceeds the length of the war itself, inconsistencies for dates are perhaps unavoidable, and it might not be fair to call them mistakes. In this case however, the writers/producers have carelessly picked a senator who only served from November 1952, making dating inescapable. As Charles, in the same episode, complains how hot it is and everyone is in shirtsleeves, it must be very late spring, perhaps May, at best, just a month before the end of the war. To emphasize the mistake, by the next episode it is late fall/early winter.