Revealing mistake: Potter is taking the driving part of the test, with Rizzo riding along. In the long shot, as well as looking at Klinger stumbling along, you can see the Jeep occupants are stunt doubles.
Continuity mistake: In the Swamp, as Hawkeye asks about Peg's cookies, BJ folds the cards in his hand, and places his left hand over the top. In the close up, as he answers, he suddenly has the cards back in a fan.
Continuity mistake: As Rizzo turns to Potter to give the test score, he puts his cigar in his mouth, and his right hand on his papers. The next shot the cigar is suddenly in his right hand.
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