When Margaret and Col. Blake are having a drink in the office, Margaret makes a comment that Henry reminds her of her father before he died. In later seasons, Margaret makes other references to her father, and in Season 9, the episode "Father's Day" has her father coming to visit.
When Margaret and Henry are having a drink in his office it is obviously daylight outside. Radar comes in and tells Henry that a company of marines has just been hit and they'll be arriving in about 45 min. By the time Henry walks outside a few moments later, it's completely dark.
When Hawkeye and Trapper are trying to sober up Margaret by giving her a cold shower, you can see that Trapper's shoulders and the front of his t-shirt are wet, presumably from previous takes.
When Margaret and Henry are in his office, drinking to celebrate her leaving, some of Margaret's hair is fastened back by barrettes. The next time she's seen, her hair is loose, without her being seen removing the barrettes.
When Henry, Hawkeye and Trapper are watching the "training film" Margaret bursts in and turns on the lights. For an 8 mm projector this would completely wash out the image on the screen yet they sit as if still watching the film.
When Margaret is in Henry's office asking for the transfer, you see a model helicopter on top of a cabinet on the right of her. It is a Bell UH-1. Although that particular helicopter was famous for medical transports in war, it didn't have it's first flight until 1956, some three years after the end of the Korean conflict. It was actually first used in action in the Vietnam conflict which became known as the helicopter war.
When the 4077th is awaiting incoming casualties, Col. Blake orders Radar to call to make sure that the helipad is ready. But it's already dark outside, and med-evac helicopters could not fly at night.
When Henry, Hawkeye and Trapper are watching the "training film" Margaret stands in the films light path to the screen blocking the image. Henry, Hawkeye and Trapper crane their heads to see the screen image which would have been on Margaret's chest.
When Hawkeye Trapper and Margaret are "toasting" in Margaret's tent, her right hand is raised. The fingernails on that hand are roughly an inch long. No nurse, especially a head nurse, would have fingernails that long.
When Hawkeye and Trapper knock at Margaret's tent, they announce themselves as "Ward and Ozzie Nelson". By 1973 when this episode aired, Ward Cleaver and Ozzie Nelson were easily recognized as the two most wholesome dads on television. However, in 1950 or 51 when this episode is set in Korea, that was not the case. While they may have known of Ozzie Nelson from radio (his radio show began in 1944, although the TV series starring the Nelson family did not debut until October 1952), Ward Cleaver did not exist at all yet, as "Leave it to Beaver" did not debut until 1957.
Henry mentions that his wife is 35 years old. But "Henry in Love," Hawkeye remarks that Henry's wife is 42. Also, in "Dear Dad Three," Henry mentioned that he met his wife at a freshman mixer. As a Lt. Col., Henry must be at least in his mid-40s, which makes 35 far too young an age for his wife.