Deliberate mistake: Winchester is listening on the radio to the 1951 Giants win the pennant. In the MASH series, Potter was supposed to have arrived 19 Sept. 1952, and Charles Winchester after Potter did. The Giants won the pennant during the previous year, not when Winchester was there. Also Potter, BJ and Winchester are present for New Years parties for '50-'51 and '51- '52 even though none of them arrived until late 1952.
Continuity mistake: When Maj. Winchester hears that the Giants won, he drops his baseball cap. A few shots later we see him lying on his back, clasping his cap in his hand.
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