Rally 'Round the Flagg, Boys - S7-E21
Revealing mistake: When Col. Flagg holds his pistol up to stop Mr. Pak Sr. from leaving, you can see there is no magazine in the pistol.
Revealing mistake: In the swamp during the movie, Frank comes up and talks to Igor, who is running the projector. Although there is a film running, there is no film on either the supply or take-up reels.
Revealing mistake: When the mail arrives in the compound, in daylight, everyone has 3 shadows. (00:00:50)
Revealing mistake: When Charlie drops the bomb on the General's jeep it is obvious that the jeep is already burnt and mangled when the explosion starts. (00:14:15)
Revealing mistake: When Baker is talking with Father Mulcahy it is clear that Baker's nose is prosthetic. The colour doesn't match as well as it does in other scenes. (00:05:45)
For the Good of the Outfit - S2-E4
Revealing mistake: Frank is shaving; when he bends down to pick up the envelope containing shrapnel fragments, the foam on his face and ear suddenly all dries up. The shot must have needed a lot of takes. (00:07:20)
Goodbye, Farewell, and Amen - S11-E16
Revealing mistake: Col. Potter is taking Sophie to the orphanage at the end of the show. "Sophie" is a male horse. Look closely.
Revealing mistake: When the tent roof caves in and the projector shorts out in a gush of water from above, you can see that actually the projector "shorts out" before the tent roof ruptures. The crew probably didn't want to risk the pyrotechnic devices getting wet. (00:02:25)
Revealing mistake: Anytime Margaret and Hawkeye are drinking in the bar, there is no liquid in the bottles.
Revealing mistake: When Hawkeye exits the tub, you can see his shorts as he wraps the towel around himself.
Revealing mistake: When Frank is digging for gold, he has 2 shadows. (00:20:00)
Revealing mistake: When Hawkeye walks into the mess tent naked as per his bet with Trapper, in some shots, you can see that he is really still wearing shorts. (00:07:40)
Revealing mistake: When Col. Potter is in the helicopter looking for a new site for the camp, you can see landscape reflecting in the canopy. This never changes position although they're meant to be flying around. (00:22:30)
Revealing mistake: In the mess, you can see everyone has their food on metal trays and ceramic dishes. Sgt Zale, though, has his lemon pie in a polystyrene dish - so that it doesn't hurt Klinger when he gets it in the face. (00:08:15)
Revealing mistake: The first scene is set in the X-Ray room. There is an X-Ray up on a lightbox in the background. Towards the end of episode 14, there is a scene in the O.R. - the exact same X-Ray is visible in the background there as well. (00:45:00)
Dr. Pierce and Mr. Hyde - S2-E5
Revealing mistake: After many hours in the OR Hawkeye takes a seat in the wheelchair that Radar's pushing, and when they reach the Swamp there's a wooden ramp on the ground right outside the door, which is never normally there, deliberately placed for this shot so Radar can push the wheelchair into the Swamp.
Nurse Doctor - S8-E7
Revealing mistake: While Charles is in the shower stall Hawkeye and BJ take his bottle of Vichy water, and when Charles steps out of the stall The Nurses outside the tent whistle, but we can see through the stall's openings that Charles is wearing something.
Hot Lips Is Back in Town - S7-E19
Revealing mistake: While Hawkeye's in the shower Radar shows up with a cup of coffee, and when Hawkeye steps out of the shower stall the door swings out so we can see the top of whatever Hawkeye's wearing.
Revealing mistake: When Hawkeye and BJ are in the showers and Margaret steals their towels and clothes, the duo head back to the Swamp naked, but we can see the top of whatever Hawkeye's wearing.
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