Continuity mistake: As Klinger and Margaret are talking about the date, he takes a sip of his drink and goes to put his hand down. After the angle changes and he goes to say his line, he repeats putting the glass down.
Continuity mistake: Margaret comes in to the Officer's Club, and tells Klinger that the drinks are on her. He puts down two glasses, and starts to pour. When the camera cuts to a close up, he's just starting to pour into the same glass again.
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