Other mistake: It's 1952 when Potter arrives at the 4077. He tells Radar that he joined the army during WWI when he was 15 (he lied about his age). That would mean that Potter was 50 when he arrives. But he said that he'd be retiring in 18 months. Also, in the episode "Point of View" Potter states that this was the first time in 37 years that he missed calling Mildred for their anniversary. That would mean that Potter was 13 when he got married.
Character mistake: When Frank is berating Igor about the food on the trays, he calls him "Sergeant." Igor has always been a private.
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