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.
Deliberate mistake: When Flagg turns out the light to escape. To make that effect they had to freeze a frame and then start again. If you look closely after Flagg turns out the light you can see Hawkeye and the Korean Man on the far right freeze. Then it shows Potter ordering the light back on.
Visible crew/equipment: When Klinger's in Colonel Potter's office wearing the fur coat and rubber reducing suit, just as Potter says, "This one is definitely in the running," we can see the shadow of the boom mic shaking up and down on the wall, at the left side of the screen.
Visible crew/equipment: When Radar gets off the phone with the guard at Panmunjom and tells Colonel Potter and BJ that Hawkeye's gone on ahead, at the start of the next shot we can see the back of the soundstage set at the top, right side of the screen. And notice that Hawkeye's and the guards' voices are echoey on the soundstage in this shot.
Revealing mistake: When Colonel Potter's in the Swamp telling Hawkeye, BJ, and Charles that surgeons' rotation points have increased from 36 to 45 Hawkeye becomes incensed, and in these two shots from this angle we can see the edge of the Swamp set at the top, left corner of the screen.