Continuity mistake: When Hawkeye and Eddie are dancing in the Swamp, after Hawkeye sits on the hot heater Eddie knocks over the tray of glasses and the mug, but next shot the mug is back up on the table.
Revealing mistake: While Hawkeye and Eddie are in the Swamp, when Eddie knocks over the stovepipe we can see that it's actually split into two pieces for the stunt, whereas in the previous shots it's not.
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