Other mistake: When Trapper and Hawkeye are driving along, you can see two points of light on the steering wheel. The lights are from from the filming illumination panels.
Other mistake: When Trapper and Hawkeye make the right turn after Trapper tries to use the restroom, you see that Trapper avoids the left side of the road just after the turn. This is to avoid the explosive charge set in the ground used to simulate a mortar round exploding.
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