Revealing mistake: In the first scene, when the camera pans back, in the upper left corner of the screen you can see that a part of the tent has been removed to make room for the camera. (00:02:15)
Continuity mistake: When Potter is on the phone, he turns to hush Hawkeye and BJ. As he does so, he's holding the receiver with his left hand, and covering the mouthpiece with his right. He then puts his left hand down on the arm of the chair. When the camera cuts in for a close up, his left hand is on the phone 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