Continuity mistake: Charles enters Col. Potter's quarters while Potter is sleeping. Potter sits up in bed while Charles whines and complains about his sister's engagement. In all the shots facing Potter, the hair at the top of his head is very messy and pointing up. In every shot facing Charles, Potter's hair is normal.
Factual error: The Chinese soldier holding the grenade in the operating theatre is speaking Japanese. (00:20:00 - 00:22:00)
Continuity mistake: When Klinger refuses to give Winchester the letter from his sister, Winchester screams at him, Klinger jumps and falls to the ground next to Winchester's bunk. After the cut, Klinger is sitting next to Hawkeye's bunk (note the airplane seat in the background instead of the door) and Winchester is holding the letter in his hand opening it. Rightfully it should be on the floor next to Winchester's bunk. If you look closely, you can see it flying out of Klinger's hand towards the door. (00:16:25)
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