Character mistake: While talking to Condon, Hawkeye and Trapper relate the story of Dr. Charles Drew, the man responsible for the storage of blood and plasma, and how he died due to not being allowed in a "whites only" hospital after being involved in horrific car accident. The true story is that he was taken to a "poor whites" hospital. Despite being black, he was admitted, and though the doctors worked diligently, his injuries were too severe, and he died. His family sent a warm letter thanking the doctors for their efforts.
Continuity mistake: During Henry's home movies of Molly's birthday party, Lorraine brings out the cake with candles and sets it on the table, but the cake differs between the shots - note the writing.
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