Factual error: Radar impersonates John Wayne, playing a scene from McLintock - a film which was not released until 1963, which was 10 years after the end of the Korean war.
Continuity mistake: While Klinger is mending the movie, the amount of film on the two reels changes a lot between shots. (00:12:20)
Audio problem: While trying to fix the projector, Klinger says, "The bulb is hot!", but his mouth doesn't move.
Continuity mistake: After the movie breaks, Hawkeye is giving an over dramatic intro to Margaret. He has his left arm raised, and a second later, both hands are at chest level.
Other mistake: When the four nurses at the door sing, two are singing, two accompanying. The nurse on the right of the shot seems to have forgotten the words.
Continuity mistake: As Klinger waves his hands to get attention for his part, it can be seen they're empty. A second later, he has a bulb in his right hand.
Audio problem: When the bulb in the projector goes out, Klinger is trying to fix it. People throw popcorn at him, saying "Find it!" After Potter says "Hit it, Father!", watch Klinger. From the wide shot to the close up, you hear him say "The bulb is hot!", but his lips don't move.
Answer: Even an Army field hospital would have SOME weapons for self-defense if the enemy attacked. What's meant is that it's not a combat outfit, and therefore wouldn't have enough weapons to actually attack anyone. (It's also mentioned a few times that the Officer of the Watch is supposed to carry a pistol at all times, but Hawkeye refuses to do it when he's in charge and Colonels Blake and Potter don't enforce the rule).
Captain Defenestrator