Rally 'Round the Flagg, Boys - S7-E21
Deliberate mistake: When Flagg turns out the light to escape. To make that effect they had to freeze a frame and then start again. If you look closely after Flagg turns out the light you can see Hawkeye and the Korean Man on the far right freeze. Then it shows Potter ordering the light back on.
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