Other mistake: When the scene is of the cow in the barn, the background hilly area can be a painted backdrop.
Other mistake: Looking at the pins when Margaret bowls at the end, the 5 pin slides backwards towards the camera, but not fast enough to bounce off anything and then fly in from off screen. Granted this was done in slow motion, but the physics don't seem to add up.
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