Other mistake: During this episode, Trapper and Hawkeye keep switching Frank's pistol with other things. When Frank's training his South Korean platoon, Trapper, Hawkeye, and Radar show up all decked out, and while Hawkeye's telling Frank that using the anti-aircraft gun on the compound will draw enemy planes, etc., there's a pistol in Frank's holster. When Frank turns around, we see that Trapper's right arm is bent over his fly swatter the entire time until he steps away from Frank, and when Frank draws from the holster what he believes is the pistol, he pulls out a plunger, and although it's funny, Trapper never actually had the opportunity to switch the pistol with the plunger, nor did Hawkeye or Radar.
Other mistake: When Frank's with Margaret in her tent and she tells him that she thinks they should reevaluate their friendship, there's a Life Magazine lying on her bed which is dated over 15 years in the future - August 25, 1967, with "The other war in Vietnam" written on its cover.
Continuity mistake: When Radar walks into Henry's office to tell him that there's a general there to see him, we get a good view of Henry's new desk and its beautiful ornate design, but later when Hawkeye and Trapper are carrying the desk and then it's lifted out by chopper it's a completely different desk - also note that this desk has casters.
Continuity mistake: The "KILROY" Hawkeye writes on the window as BJ looks out was in the center with his fingertip. Later, as Hawkeye looks out, the "KILROY" is now closer to the frame, and the lettering is different, a small capital A in front of it, and lines above and below it.
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.
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.'