Continuity mistake: After Hawkeye and Burns drive through the puddle, the mud on the colonel's face is different in the long and closeup shots. (00:02:00)
Continuity mistake: When Frank inspects the local workers, the laundry woman bends down to help the kid put away the sandwich Burns suspected of being a bomb. After the cut, she's upright again. (00:10:45)
Factual error: In the hut with BJ, Zale, and The Moose, there's a Coleman 413E stove in the background. Trouble is, that this unit didn't appear until 1954, and the Armistice ending hostilities, ending the war, was signed July 27, 1953.
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