Continuity mistake: Early in the episode a tank is driven into the MASH compound by a wounded soldier (demolishing the latrine in the process). The tank is an M24 Chaffee dating from the mid 1940s - it is squat and angular in shape. Later on in the episode after the tank has been hidden under a tent Hawkeye decides to drive the tank into the camp dump (demolishing the new latrine on the way). The tank has changed into an M4 Sherman - it is a lot higher and more rounded in shape.
Revealing mistake: Toward the end of the episode, Henry is talking to a general on the phone when the chopper is coming in. He's trying to tell the man that he can't hear him. As he continues trying to talk, he gives up, and hangs the receiver up on the skeleton's head. If you look, you can see the hook that was conveniently placed for the gag.
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.
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.
Factual error: The MP describes the antique vase Burns is supposed to have bought as "An 800-year-old seladon vase of the Ko-Yu dynasty". Later, Burns packs up a white vase to send to his wife. Seladon is by definition green, and that kind of color glazing definitely wasn't around in the 13th century. What Burns packs up looks most like early to middle Quing period - or rather a contemporary ripoff.
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.'
Revealing mistake: When Radar carries the field phone from Col. Potter's desk over to Hawkeye who is squatting in the corner, the phone doesn't have a phone line attached. It is an EE-8 Military Field Phone, which is a wired device, not a radio - even if Radar elsewhere says he has somebody "on the radio" when in fact he is using an EE-8.
Continuity mistake: As Hawkeye climbs under the table to hide there are three small stacks of white bandage boxes on the table. When the shelling starts, all the boxes in two of the stacks fall off the table, leaving one stack. When the shot changes, there are suddenly two stacks of boxes on the table.
Factual error: Henry says that every Wednesday, his wife drives up Route 26 with some friends. US. Route 26 starts out in Nebraska and leads to Oregon. The closest thing that could be described as a "Route 26" would be the road leading from Princeton, IL to Dixon, IL which begins 85 miles from Bloomington. The writer probably meant Route 24, which passes about 20 miles north of Bloomington.