Character mistake: After Potter mocks Hawkeye for not hitting anything, Hawkeye replies "You fired as many shots as I did". In fact, Potter fired seven shots, Hawkeye only five. On a side note, this also suggests that Hawkeye probably was supposed to fire seven times, but his weapon jammed after the fifth shot. (00:22:00)
Character mistake: As Potter and Hawkeye pull up to the MP checkpoint, Potter and the MP exchange salutes. As per Army regulations, no salutes are given under battle conditions. The reason is that if the superior officer, in this case Colonel Potter, returns the salute, he can be a target for snipers.
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