Plot hole: Hawkeye calls a number of people into the mess tent over the PA - the ones he allegedly suspects of being behind the thefts he is suspected of himself. Interestingly enough, Ho Jon, later revealed to be the guilty party, is not on Hawkeye's list - yet he shows up uninvited, just to be ensnared by Hawk's clever ploy. Note also that he had no way of knowing what the purpose of the meeting was, so we cannot ascribe to him the motive of wanting to find out how much Hawkeye knew.
Suggested correction: Of course Ho-Jon would come to the tent; it makes perfect sense, since he is the "houseboy" of the Swamp and, consequently, a sort of personal assistant to the Swampmen (Hawkeye, Trapper, and Spearchucker). He simply followed Trapper and Spearchucker to the tent after the announcement, probably figuring they might need him in some way.
It's late evening. It's, as far as anyone knows, an official meeting. Ho Jon isn't "standing attendance", he's sitting at the table (which is very convenient for him to hide his hands later). If he WERE standing attendance, it would be the only time in the series he does so in the mess tent instead of the swamp. It would also be the only time he's attending a meeting anyone called. Also he isn't a "house boy" - that would be totally out of character for Hawkeye, see "The Moose" - he's more an adoptee and roommate who makes himself useful. And last but not least: What a convenient coincidence, that just the guy who turns out to be the culprit would turn up uninvited, because he "might be needed" instead of staying the hell away because he is guilty and suspicious of the whole affair! Had - HAD, which he hasn't - Trapper said "Ho Jon, you better come too", you could call it a Deus Ex, but the way it is, it's just a plot hole, to quote Margaret Houlihan, "period, end of sentence."
Plot hole: When the truck with the orphans arrives, Col. Potter and Nurse Cratty greet each other like one would an old friend. Being new to Korea, Col. Potter doesn't know Nurse Cratty - as becomes clear from his reaction to Hawkeye's explanation to BJ earlier (who doesn't know Nurse Cratty for the same reason, but that's not relevant for this mistake). Note that in other parts of the series Col. Potter is depicted mostly as somewhat old-fashioned and reserved towards strangers. (00:05:20)
Plot hole: This episode revolves around the doctors trying to "transfer" a north Korean surgeon to the outfit. To this end, they get him papers, uniform, dog tags, etc. In the end, the plot is toppled and The Korean Surgeon taken to a POW camp by the MP. In reality, it would not have ended quite so pleasantly. A combatant wearing the uniform of an enemy is usually automatically considered a spy, and Hawkeye, BJ and Radar would also have been considered guilty of espionage or at least complicity therein.
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. (00:12:45)
The Merchant of Korea - S6-E14
Plot hole: In this episode, the military money, or scrip, is being called in and exchanged for a different color (and assumedly design - otherwise counterfeiters could just keep using their printing plates) to battle counterfeiting. However, in previous episodes several colors of scrip are being used equally and at the same time - e.g. in episode "Hey, Doc" (4-5), Sgt. Kimble collects a pot consisting of both blue and tan one-dollar scrip notes. No previous indication was given in the show that the army started a practice of using just one color at a time.
Patent 4077 - S6-E16
Plot hole: When Hawkeye and BJ buy Margaret a new ring, it takes a typo in the inscription to give them away - which makes both of them and Mr. Shin almost clairvoyant. Not only did they somehow guess Margaret's ring size, but Mr Shin - phew, Houdini and Uri Geller together don't hold a candle to this guy - actually somehow divined the exact type and font of the inscription in the original so perfectly that Margaret actually only spotted the difference from the missing 'n.'
Yessir, That's Our Baby - S8-E15
Plot hole: Charles has the money and family connections. Why didn't he try to get the baby girl sent to the US? Trapper and his wife almost adopted a seemingly orphaned Korean boy in an early episode, so it couldn't have been impossible.
Suggested correction: There is a difference between adopting a child and merely sending it to the States without any support system to be put into an orphanage.
Plot hole: In this episode, Margaret is required to give a lecture on the use of Levophed, because it is being introduced. However, in the Episode "Period of Adjustment"(8-6), Hawkeye orders an IV of Levophed for one of his patients. (00:12:15)