Springtime - S3-E6
Factual error: Radar mentions to a nurse he's smitten with that the movie that night is "Firstborn of Godzilla." Godzilla (the movie, not the monster) wasn't released until 1954. (00:15:10)
Springtime - S3-E6
Other mistake: While Radar is measuring the camp, he says that last year they had 2,986 square feet, but this year they have 2,863 square feet. The square root of 2,863 is about 53.5, so unless the camp is 53 feet by 53 feet (!) his numbers are WAY off. (00:16:15)
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