Factual error: In surgery Trapper John is singing Frank Sinatra's version of "I got you under my skin". Although it was written in 1936, Sinatra did not release it until 1956, after the Korean War ended. The 1936 version sung by Al Bowlly sounds nothing like the version Trapper John was singing, which was mimicking Sinatra's version.
Suggested correction: While it hadn't been released on vinyl until 1956, Sinatra had sung the song as early as 1946 on his radio show and during live shows.
The version Frank Sinatra sang on his radio show was similar to the original version used in the movie "Born to Dance" (a movie he references before singing his two songs). He didn't change it to the big band version that Trapper imitates until 1956.
Factual error: The apartment makes no sense.There are 3 steps down to the living room which you might have in a house but not in a high rise apartment building.The hallway shows a door for another apartment which would put most of its apartment out past the edge of the building.
Factual error: 2016 special - You Can't Teach An Old Dog New Tricks: Mr Harmon comments on a perfume called Belle, which he thinks is called "Belly", "I wonder what the next one will be called. Bingo Wings?" The episode is set in 1988 and the term "bingo wings" didn't exist before the 1990s. (00:10:40)
Factual error: During the meeting with American prisoners the lone woman says she's fought in both the European and Pacific theaters. Unless I'm mistaken, nobody got shipped from one to another during the war unless one theater was done.