Continuity mistake: When Hawkeye is examining the orphan who is wiggling his tongue, there are two camera angles: one of Hawkeye from the front and one of the orphan over Hawkeye's shoulder. In the first shot, the tongue depresser that Hawkeye is holding is horizontal, in the other it is vertical. This flips back and forth a couple of times. (00:06:30)

Continuity mistake: When Margaret pins on Frank's purple heart, his scrubs are very damp with sweat. When he enters the swamp, they're practically dry. (00:03:50)
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