Hawkeye puts Trapper back to bed, only to learn that more casualties on en route. As he slams Trapper's shirt down to the floor, you can see Margaret kneeling beside Frank's bed. Frank doesn't have a towel on his forehead. In the next shot, there is a towel on his forehead.
During this time period no nurse would be put in as CO of a medical outfit even if the nurse ranked higher than the Dr..
The PA announcement says that a Nobel Peace Prize has been awarded in Stockholm, Sweden. The Nobel Peace Prizes have always been awarded in Oslo, Norway.
The news update over the loudspeaker refers to the Vietnam War. The Vietnam War started in 1954 approximately a year after the Korean War ended.
When nurse Jacobs is in the changing room, her fingernails can be seen at over 1/2 inch long. No nurse would have such long fingernails.
In the final OR scene the PA announcement can be heard mentioning that "the French Army predicted a swift end to the Vietnamese War", even though care was taken during the entire series to avoid any reference to that conflict. The announcement refers to the First Indochina War between France and the Viet Minh 1946-1954.
In the office Radar says to Hawkeye " I suppose you realize you're ranking surgeon now". As chief surgeon, Hawkeye is already the ranking surgeon.
When Hawkeye and Margret are in Colonel Blake's office there is a UH-1 Helicopter on the top shelf. The Huey was not introduced until 1959, about 7 years after the scene takes place.
Margaret says, "Let me get at your hip" as Hawkeye drops his pants and bends forward for her to inject the flu vaccine into his rear end. The hip is located at the front, not the rear. A nurse like Margaret should know that.