Factual error: When Frank sits down on Margaret's bed, he pulls a single metal star out of his butt. Kelly being a Lt. Gen, he should have (and has, as can be seen in other scenes) a single bar of three interconnected stars, not three single ones. Therefore Frank shouldn't be able to find a solitary star in Margaret's bed. (00:19:00)
Factual error: Radar gives the location of the battle as Longitude 70, Latitude 27. This means the Korean war has spread to India. (00:21:00)
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