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)
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.
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.
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