Visible crew/equipment: After the scene in the x-ray room with Henry asking Hawkeye and Trapper to "read between the lines" in the letter from Henry's wife, when it cuts to Radar on the phone the shadow of the boom mic can be seen on the wall at the top left side of the screen, right before it's pulled up.
Audio problem: As Trapper opens the door to the swamp and the football flies in, a splash is heard as if it hit a tub of water, followed by the sound of a high, fluted vessel filling with water. Neither of those sounds make sense in this case. (00:07:00)
Factual error: Radar finds a rabbi on board USS Essex, but the film shown of the Essex isn't...it's the USS Yorktown CV-10.
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