Continuity mistake: Just after the announcement that General MacArthur is coming, Trapper puts on his sunglasses, then the shot switches to Henry walking, and in the background Trapper is putting his glasses on again.
Visible crew/equipment: As Col. Whiteman leave Sentry Post 1, where Klinger is, the boom mic is reflected on his helmet.
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