Continuity mistake: The mud spots on Lt.Smith's face change from scene to scene. (00:09:45)
Continuity mistake: As Lt. LeClerq stands beside his commander, the Commander starts to look to his left, and drops his hand. When the angle changes, he drops his hand again.
Continuity mistake: The syringe the "Mad Turk" threatens Henry with alternates between fully ready to almost empty between shots.
Continuity mistake: As he addresses Maj. "Chicken Lover", Lt. Smith's head goes from leaning left to leaning right between shots.
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