Visible crew/equipment: While in the mess tent, after Margaret's grossed out by the smell and walks away we hear Charles start playing again, and when Colonel Potter says, "Just make sure the three of you work this out fast," in this shot we can see the actor's T-mark on the floor between Potter and Hawkeye, where Margaret stood a moment ago.
Audio problem: After Potter convinces Saunders he still wants to live, the hiss from the anesthesia machine fades out even while Potter and Saunders are still standing next to it. Neither Potter nor Saunders turned off the valve again.
Revealing mistake: When Margaret whistles for the "third wave" she places Winchester's French horn on the ground, and there are three shots facing the jeep as it closes in on the horn - in the first two shots the horn's normal, but in the last shot the horn's already semi-squashed before the jeep even runs over it.
Continuity mistake: When the Jeep runs over the French horn, the crowd is a good distance back. When Potter comes out and picks up the flattened horn, the crowd is only five or six feet away without having moved up.
Continuity mistake: When BJ and Hawkeye are arguing while trying to eat, Winchester starts his French Horn. When the camera is behind BJ, he puts down his fork. When the camera cuts to a front shot of BJ, he's holding the fork he just put down. Then the camera cuts to look at Hawkeye, BJ's fork is down 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