Continuity mistake: When Frank walks into the Swamp and puts down the typewriter, in shots facing Frank the manila envelope's open flap faces up, but in shots facing Trapper and Hawkeye while they're pretending to argue the envelope is flipped over with the flap facing down, then when Frank walks back to the envelope the flap faces up.
Continuity mistake: While Hawkeye and Trapper are playing shotglass checkers Frank lathers shaving cream onto his face, but in his closeups the thick foam is dried out.
Continuity mistake: While Trapper and Hawkeye are lying on their cots, one by one everyone joins them in the Swamp, and in Trapper's closeups the "USA sterilized" that's printed on his pillow is upside down, but in the wideshots his pillow's flipped over with the print right-side up.
For the Good of the Outfit - S2-E4
Continuity mistake: While Radar and Hawkeye are in the mess tent, after Hawkeye cracks a joke about how the cook sculpts grease into the shape of lamp chops, between shots facing Radar and the shots facing Hawkeye we see Radar either holding bread in his right hand or a fork.
Continuity mistake: When Trapper and Hawkeye are sitting outside the Swamp, Hawkeye pours the martinis from the tall glass beaker, and in the shots facing Hawkeye there are quite a few large ice cubes in the beaker, but in the shots facing Trapper there aren't as many ice cubes floating in the beaker.
Continuity mistake: When Klinger's stopped by the MPs it cuts to a close-up of the Polaroid camera and it's lying between the seats with its hand strap facing the front of the jeep, but when Klinger picks it up the camera's positioned the opposite way with its hand strap facing the back of the jeep.
Continuity mistake: While Colonel Potter is painting the portrait of Charles, the portable military field desks behind Potter are all open - note the front doors are flipped down, but in the closeup of Charles holding the painting of himself the doors are folded up. And the books, etc. atop the field desks change as well.
Continuity mistake: While BJ, Hawkeye, and Margaret are in the OR, BJ has the stethoscope either around his neck or the eartips are in his ears, depending on the angle of the consecutive shots.
Continuity mistake: When Colonel Potter, BJ, Hawkeye, and Charles are in the changing room, Charles wants to be alone so he takes his tan jacket off the first nail on the right and leaves, but in BJ and Hawkeye's closeups the tan jacket is still hanging on that first nail, then it vanishes again.
Continuity mistake: When BJ and Hawkeye are peeking into Radar's box of bees, in the wideshot there's tape on the box, but in the closeup the tape has vanished.
Continuity mistake: When Hawkeye and Radar leave the 4077 in the jeep, the last three numbers on the hood are "717" but when they get to Kimpo it's a different serial number ending in "388."
Continuity mistake: When Radar and Hawkeye leave the 4077, the jeep they're in has its windshield in the fold-down position over the hood, but in the two shots from behind Hawkeye and Radar when they see the checkpoint up ahead and Hawkeye speeds up, the windshield has vanished and there's a star on the hood.
Continuity mistake: After speeding past the checkpoint Hawkeye's stopped by the MPs, and when the lieutenant takes hold of one of Hawkeye's dog tags he's holding the one on the extender chain, but next shot he's holding the other dog tag, with the extender chain and second dog tag hanging down.
The Trial of Henry Blake - S2-E8
Continuity mistake: When Radar walks into the Swamp to sell wingtip shoes to Hawkeye, the dartboard isn't hanging on the door, but in two of Radar's closeups we can see part of the door with the dartboard on it.
L.I.P. (Local Indigenous Personnel) - S2-E7
Continuity mistake: After Lieutenant Willis wakes up in the Swamp he gets dressed and puts his tie around his neck with its tail end on his right, but when it cuts to his closeup the tie's wide end is at his right side, then it switches again.
Continuity mistake: When Hawkeye's saying goodbye to the nurse in the morning, he reads "35591715" from her dog tag and says, "Even your number is pretty," and then he makes another date with her and again reads her dog tag, but now the number's "39591715."
Dr. Pierce and Mr. Hyde - S2-E5
Continuity mistake: After Hawkeye and Trapper leave the OR, when they open the door to the Swamp the dartboard is not hanging on the door, but in the interior shot the dartboard's there.
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.
Continuity mistake: During the charity no-talent night, when the curtain opens on the Swinging Surgeons we can see Radar using a set of brushes on the drums, but in Radar's closeups he's using drum sticks, then in the wideshot it's back to the brushes again.
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