Factual error: In the Swamp, Frank is complaining about everything, and goes to grab the still. The stove it's sitting on is a Coleman model 413E camping stove, a unit not seen until 1954, and the series takes place in 1950.
Continuity mistake: Casey's glasses go from dark framed to metal framed and back as he says goodbye to Hawkeye.
Love Story - S1-E14
Continuity mistake: When Trapper puts on the "Dear John" recording, the record is moving at two different speeds in the close up and wide shots.
Continuity mistake: While Hawkeye holds the tail assembly, Trapper cuts the wires. In the closeup, he cuts the wires a few inches from the connectors. In the wide shot, the wires were cut closer to the bomb's body.
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.
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.
Love Story - S1-E14
Visible crew/equipment: After Radar tells Margaret that she's needed in the post-op ward Frank sneaks toward Margaret's tent, and when it cuts to Margaret walking into post-op, at the start of the shot we can see the two actors' curved chalk foot marks on the floor.
Love Story - S1-E14
Other mistake: After Hawkeye asks, "Radar who?" while he's kissing a nurse, it cuts to Trapper, Radar, and Hawkeye walking past a jeep parked in front of the mess tent, then another jeep shows up with Lieutenant Anderson, but both jeeps have the same stain (looks like rust) on the front bar - the same jeep was used in both shots.
Continuity mistake: When Hawkeye and Eddie are dancing in the Swamp, after Hawkeye sits on the hot heater Eddie knocks over the tray of glasses and the mug, but next shot the mug is back up on the table.
Revealing mistake: While Hawkeye and Eddie are in the Swamp, when Eddie knocks over the stovepipe we can see that it's actually split into two pieces for the stunt, whereas in the previous shots it's not.
Henry, Please Come Home - S1-E9
Other mistake: While Radar's in post-op waiting for Henry's arrival he's seen reading Marvel Comics "Captain Savage and His Battlefield Raiders!" issue #10, published January 1969. It's one of the 19 issues in this comic book series which were originally named "Captain Savage and His Leatherneck Raiders," and it ran from 1968 until 1970, many years after the Korean War ended. This comic is also seen in the episode "Tuttle" later this season.
Visible crew/equipment: When General Barker opens the doors to Henry's office and finds Radar sitting behind the desk, we can see Barker's curved chalk foot marks on the floor beside the desk, where the actor will stand in a moment.
Other mistake: At the end, after General Barker tells Henry that he should give Frank a high colonic and send him on a 10 mile hike, Klinger shows up in front of them supposedly naked, but we can see the top of whatever the actor's really wearing.
Continuity mistake: This episode has the heater in Henry's office in front of the window, and the wall by the window blank. Later the stove is by the window, with the diploma by the stovepipe.
Requiem for a Lightweight - S1-E3
Audio problem: When Margie is saying she is impressed, Trapper replies "I should hope so", but his mouth doesn't move.
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