Revealing mistake: When Hawkeye and BJ are in the showers and Margaret steals their towels and clothes, the duo head back to the Swamp naked, but we can see the top of whatever Hawkeye's wearing.
Continuity mistake: Charles arranges a prank that involves a cake. The cake looks totally different in the respective shots. At least three cakes were involved: The one Klinger gives to Margret looks different from the one she holds in her hands when walking over to Capt. Hill. The one she holds in her hand in the closeup counter shots is yet another pie.
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