Dr. Pierce and Mr. Hyde - S2-E5
Revealing mistake: After many hours in the OR Hawkeye takes a seat in the wheelchair that Radar's pushing, and when they reach the Swamp there's a wooden ramp on the ground right outside the door, which is never normally there, deliberately placed for this shot so Radar can push the wheelchair into the Swamp.
Dr. Pierce and Mr. Hyde - S2-E5
Continuity mistake: After Hawkeye and Trapper leave the OR, when they open the door to the Swamp the dartboard is not hanging on the door, but in the interior shot the dartboard's there.
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