Hawkeye makes a reference to Nedick's in Grand Central Station (New York City). It was a fast-food chain on the East Coast of the US, selling hot dogs, doughnuts, coffee, and a signature orange drink. It was in business from the 1920s to the 1980s.
When Hawkeye and B.J. unwrap Peggy's cake, Hawkeye reads on a newspaper used for the wrapping that Elizabeth Taylor married someone who's name begins with N-I. This is her first husband Nicky Hilton, of Hilton Hotels fame. They married on May 6, 1950.
The subplot in which Colonel Hollister forces Mulcahy to write a letter to a patient's family telling them all is well is reminiscent of a subplot from the original novel, in which the Swampmen object to a Protestant chaplain's habit of ghostwriting cheerful letters for patients without checking the severity of their wounds. The main difference here is that the patient doesn't die, and the Swampmen don't lash the chaplain in question to a cross and make him believe they intend to burn him alive.
One of the phrases Frank attempts to teach the Koreans is "Don't contaminate our drinking water with fluoridation." In the 1950s and 1960s, conspiracy theorists claimed that fluoridation was a communist plot to undermine American public health. Frank's use of this phrase suggests that he believes in the conspiracy theory.
In one scene, Hawkeye and BJ are playing chess. Hawkeye mentions the "Zuckertort Attack". Johannes Zuckertort was a 19th century chess master.