Factual error: In the Swamp, Frank is complaining about everything, and goes to grab the still. The stove it's sitting on is a Coleman model 413E camping stove, a unit not seen until 1954, and the series takes place in 1950.
Factual error: Hawkeye and Trapper are concerned about the theft of a stock of hydrocortisone, but that drug wasn't introduced by the FDA until 1952.
Sometimes You Hear the Bullet - S1-E17
Factual error: We see Pvt. Wendel trying to hot-wire a jeep to escape. He wouldn't have to hot-wire it, because vehicles assigned to a combat zone were equipped with an ignition switch, not an ignition lock, for the simple reason that keys get lost or mislaid all the time and in an emergency, having to track down keys for vehicles would be extremely detrimental to an unit's combat effectiveness.
Factual error: The announcer says that it will be the 53rd Army-Navy game, but the game has been played every year since 1890, with no games in the years 1894-98, 1909, 1917-18, and 1928-29, so this game would be number 51. Additionally, at the end of the episode we find out the result was Navy 42 - Army 36. While Navy won all three games during the Korean conflict, none of those games ended with such a score. The score in the 1950 game was 14-2.
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