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.
Upvote valid corrections to help move entries into the corrections section.
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.