Character mistake: During The Interview in the Officer's Club, after Rizzo gets the West Point question wrong, Charles dismisses him by saying, "Thank you, Corporal, that'll be all." Rizzo is a Staff Sergeant (SSG) according to his sleeve.
Audio problem: In the Post-Op ward, Jimmy is playing poker with the two jerks in his platoon. After the cards are dealt, he sees that their deck has pictures of nude women. He looks up at them when seeing this, and you hear him say "Very funny!", but his lips don't move.
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