Revealing mistake: The first scene is set in the X-Ray room. There is an X-Ray up on a lightbox in the background. Towards the end of episode 14, there is a scene in the O.R. - the exact same X-Ray is visible in the background there as well. (00:45:00)
Continuity mistake: As the camera looks at the door of the Officer's club while the General and Hawkeye talk, other tents can be seen behind them. As Hawkeye brings in the enlisted personnel, the area is totally empty.
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