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Other mistake: When Henry gives Leslie the gift he says, "I sent to Tokyo for this... A Sato Tanaka double-cammed reel with jeweled escarpment," and we can see on different sides of the box there's green tape hiding its brand name, "Penn," though we can still make out the "Beachmaster 155" name.
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