Continuity mistake: While Radar's spying on Baker's hand for Hawkeye during the poker game, Baker's only wearing his T-shirt later in the game, but in the views from Radar's telescope eyepiece Baker's still wearing his jacket.
Continuity mistake: After Frank picks up the still, his hands alternate from left hand above right to right hand above left between angles.
Requiem for a Lightweight - S1-E3
Other mistake: At the end of the show Trapper has a steak over his eye covering the black eye he received. Throughout the series the characters constantly complained about the food yet they have the audacity to waste a perfectly good steak.
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.
Audio problem: At the end, while Radar is playing drums, he is using drumsticks but drum brushes are heard.
Sometimes You Hear the Bullet - S1-E17
Continuity mistake: Hawkeye lifts Wendell's arm, takes his pulse and lays his arm down by his side again. In the next shot, Wendell's arm is across his chest. (00:13:55)
Sometimes You Hear the Bullet - S1-E17
Continuity mistake: As Frank receives his purple heart, Henry calls him 'Franklin D. Burns' All other references to his full name in the series give his middle name as 'Marion'. (00:23:50)
Revealing mistake: When Frank is digging for gold, he has 2 shadows. (00:20:00)
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 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)
Continuity mistake: When Frank is getting drunk he spills gin down the front of his vest. A few shots later, just before he collapses, it suddenly dries out significantly. (00:13:20)
Sometimes You Hear the Bullet - S1-E17
Continuity mistake: Frank and Margaret are dancing in her tent when Frank's back seizes up; in the subsequent shots sometimes his arms are around her waist and sometimes around her shoulders. (00:02:30)
Continuity mistake: At lunch, when Frank is getting his own back against Hawkeye, in the long shots of the table the plate of bread is beside Henry and in the closeups it is in front of Trapper. (00:11:30)
Sometimes You Hear the Bullet - S1-E17
Other mistake: Wendel, afraid of being shipped home, is trying to escape from the MASH by hot-wiring a Jeep. Despite just having had an appendectomy, he is leaning forward and to the right from a sitting position, which would have to put pressure directly on the incision, yet when discovered by Hawkeye, he easily and without discomfort sits up straight. Aside from him still being at the MASH, we know the surgery is recent because, just a little later, he winces and complains after making a very small movement.
Audio problem: The original "gin machine" is entirely metal, but when Frank throws it on the floor, you hear porcelain breaking.
Other mistake: While the dentist is working in Henry's mouth Frank's describing Hawkeye and Trapper's pranks, and right after we see a shot of the dog licking hamburger from Frank's ear, when it cuts to Henry saying, "Frank, just leave my married life out of this. Doc, will you watch it before I swallow your watch!" keep your eyes on Larry Linville as he mouths McLean Stevenson's lines along with him.
Other mistake: When Hawkeye walks into the shower tent while Ugly John's showering he removes his robe, and just as Hawkeye swings open the door to step into the shower stall we can see that he's wearing something, presumably a swimsuit.
Continuity mistake: In the mess tent, after Radar uses the ketchup he puts the cap back on, but while Hawkeye and Trapper tease Radar about his hearty appetite, when it cuts to Radar's closeups the cap is off the ketchup, but then it's back on in the wideshot.
Continuity mistake: After the opening credits it cuts to Hawkeye, Trapper, Radar, and Ugly John playing poker in the Swamp and they're all wearing their uniforms when they run out to the incoming choppers, but what we see next is the same footage from the Pilot that's shown in the opening credits, with Hawkeye and Trapper wearing Hawaiian shirts as they meet the choppers.
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