Other mistake: When Henry is trying to convince Baker how wonderful the camp is, Henry says that they "had 'The Thing' and 'The Blob' both in one week." The movie "The Blob" was made in 1958. This season of M*A*S*H is set in 1951 and 1952 (and the war ended in 1953). (00:03:55)
Revealing mistake: When Baker is talking with Father Mulcahy it is clear that Baker's nose is prosthetic. The colour doesn't match as well as it does in other scenes. (00:05:45)
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