Continuity mistake: When the pit boss is taking the rolled up 5 containing the pair of dice out of his pocket, his fingers are hiding the end toward Mulcahy. When the camera angle changes, the fingers are moved so Mulcahy can see the hidden dice.
Revealing mistake: During the melee at Rosie's, after Klinger gets his money and jewelry back from the cheats a guy is thrown through windows, and though we hear the sound of smashing glass we see the shreds of plastic fluttering.
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