Mad Dogs and Servicemen - S3-E13
Other mistake: Hawkeye, Henry and Trapper are playing scrabble. The board is in an illegal state - in the lower right corner 'it', 'jot', 'joy' 'yearn' and 'in' are not connected to the rest of the words. Since the others call Hawkeye on his non-existant word, I'm assuming they're playing properly. (00:15:35)
Mad Dogs and Servicemen - S3-E13
Factual error: While Radar's lying in bed, Margaret reads a letter to him which was written by Wanda McCandless, and in the letter Wanda mentions that her favorite songs are "Pretty Thing..." by Bo Diddley, and "Oh, The Wayward Wind..." by Gogi Grant, but the problem is these songs were written and recorded in 1955 and 1956, years after the Korean War was already over in 1953.
Mad Dogs and Servicemen - S3-E13
Visible crew/equipment: As the medics take a stretcher off The Bus, and then Hawkeye goes into The Bus, the shadow of the recording equipment boom plays across them.
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