Hot Lips and Empty Arms - S2-E14
Continuity mistake: Margaret is in Henry's office drunk and she tells Henry that he looks just like her father did before he died. In Season 9. Episode 4 "Father's Day" Margaret's father, Alvin 'Howitzer' Houlihan, visits her at the 4077.
For the Good of the Outfit - S2-E4
Continuity mistake: Henry pops out the golf ball he is washing into the towel. After he finishes talking to Hawkeye, he resumes washing. However, no ball is missing from the dirty pile. (00:02:45)
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)
The Trial of Henry Blake - S2-E8
Continuity mistake: In the scene of Klinger trying to escape from the 4077 on a hang glider, he secures himself into the control frame, but then when he takes off, he's hanging off the frame's bottom bar. (00:10:40)
Visible crew/equipment: While Radar is in Henry's office with the woman and her baby, being teased by Trapper and Hawkeye about the possibility of him being the father, just as Frank walks into the office a crewmember's hand can be seen between the two doors near the floor, preventing the closing door from swinging.
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.
Visible crew/equipment: Before the meeting in Henry's office starts, when Margaret and Frank take their seats, under Frank's chair we can see the chalk T-mark on the floor behind him.
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.
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.
Visible crew/equipment: When Dr. Freedman's in Henry's office before Klinger walks in, just as Henry says, "You're the doctor," the shadow of the moving boom mic can be seen at the top left side of the screen.
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.
Visible crew/equipment: While in the mess tent, when Henry introduces Hildebrand to Margaret it cuts to Henry as he says that she's the best head nurse in Korea, and at the top right corner we can see the open edge of the tent set and what's behind it.
Hot Lips and Empty Arms - S2-E14
Visible crew/equipment: When Margaret walks into Henry's office while Trapper, Henry, and Hawkeye are watching a "training film," the actor's chalk T-mark can be seen on the floor.
Visible crew/equipment: After Radar walks into the Swamp and gives Hawkeye and Trapper the coffee and case folders, just as Radar tells them that he was too sleepy he walks out, and the actor's chalk T-mark can be seen on the ground (although faint, it's distinguishable).
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."
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