Continuity mistake: After Klinger throws his ball, his arm stays extended outward. As the shot cuts, looking down the lane towards him, his arm is hanging straight down. Then, after the strike, he raises both arms up. A second later, his left arm is down by his side, his right doing a celebratory motion.
Revealing mistake: During the conversation between Potter and Klinger in the Mess tent, if you look past them you can see Margaret loitering, waiting for her cue to enter.
Other mistake: Looking at the pins when Margaret bowls at the end, the 5 pin slides backwards towards the camera, but not fast enough to bounce off anything and then fly in from off screen. Granted this was done in slow motion, but the physics don't seem to add up.
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