Continuity mistake: After Hawkeye and Trapper cut the bomb wires, Trapper kneels down to see if it's still ticking, and his hand disappears from his helmet. (00:23:05)
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.
Continuity mistake: Right after Radar tells Henry to forget about the game there's an explosion, and when Radar shouts, "More on the way!" everyone ducks and we see Henry's diploma up on the wall, but when it cuts to a different angle the diploma has vanished before the room even shakes or the heater's stovepipe falls.
Other mistake: During the game, when the second bomb goes off, the whole building is shaking and things are falling all around but the drinks on the table do not move at all.
Revealing mistake: When the second shell explodes outside, the shelf in the right foreground shakes a moment, then the top suddenly flips up, dumping the bottles that were on it. Obviously a stagehand flipped it when no bottles fell.
Other mistake: Hawkeye reads the propaganda flyer, he says. "Give yourselves up, you can't win. Douglas MacArthur." Trouble is, the papers are all advertising for a flying company called Ace Eli.
Continuity mistake: While Hawkeye holds the tail assembly, Trapper cuts the wires. In the closeup, he cuts the wires a few inches from the connectors. In the wide shot, the wires were cut closer to the bomb's body.
Other mistake: Hawkeye loosened the nut and locking ring, but after lifting the assembly, it was obvious that these were steps used only to heighten tension. There was no locking device of any kind between the tail and body of the bomb.
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