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.
Visible crew/equipment: After Charles confronts Choi Sung Ho about the candy, Ho explains that he sold it on the black market to buy real food, and when Ho reenters the mess tent through the side door, we can see that outside there's a director's chair, which actors also use, with something printed on its back.
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.
Factual error: While watching the Sonja Henie movie "Sun Valley Serenade" Colonel Potter says at one point of the movie "This is supposed to be where she does a triple axel and ends up in a split." Then he has to leave and says "Now I'll never get to see it." He wouldn't be able to see it until 1989 when Midori Ito from Japan was the first woman to complete a triple axel in competition, Tonya Harding was the 2nd woman to complete one and the only American woman. And I doubt Sonja Henie ever did anything as complicated as a triple axel even with her 3 Olympic Gold Medals.
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.