Continuity mistake: While Radar's spying on Baker's hand for Hawkeye during the poker game, Baker's only wearing his T-shirt later in the game, but in the views from Radar's telescope eyepiece Baker's still wearing his jacket.
Other mistake: When they're playing poker, Hawkeye is sitting at an angle so that Sgt. Baker cannot see the earpiece that Hawkeye is wearing. However, Hawkeye sometimes turns his head enough for us to see his ear and, since the camera angle is over Baker's shoulder, Baker must have been able to see the earpiece too and realise he was being cheated. (00:13:20)
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