Continuity mistake: When Mulcahy is describing a person who was "quite a Bozo" to Potter, Potter realizes who he is referring to. Mulcahy's arm is close to the table. When the camera cuts to Mulcahy's face, his mug is close to his face.
Continuity mistake: When Potter is chewing out Klinger about the morning reports, the camera is looking at Potter. As he finishes his line with "once in a while", he puts his right arm down. When the camera cuts to look at Klinger from behind Potter, his (Potter's) arm is up and finger pointing at Klinger.
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