Revealing mistake: When the mail arrives in the compound, in daylight, everyone has 3 shadows. (00:00:50)
Visible crew/equipment: After Hawkeye and Trapper tell Frank that they made up Pioneer Aviation to help him look foolish, when Hawkeye picks up Trapper's duffel bag, as the shot pulls back the chalk T-mark can be seen on the floor where Hawkeye had been standing.
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