Nurse Doctor - S8-E7
Revealing mistake: While Charles is in the shower stall Hawkeye and BJ take his bottle of Vichy water, and when Charles steps out of the stall The Nurses outside the tent whistle, but we can see through the stall's openings that Charles is wearing something.
Revealing mistake: When Sherwood has died on the gurney, with Roberts holding his hand, after breathing stops, you can see the bandage on his neck still jumping in time with his pulse.
Revealing mistake: Anytime Margaret and Hawkeye are drinking in the bar, there is no liquid in the bottles.
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