Getrude Stein refers to 'science fiction'. In the 1920s, the usual term was 'scientific romance', although Hugo Gernsback (editor of the first sf magazine, Amazing Stories, first published April 1926) unsuccessfully attempted to popularise 'scientifiction'. 'Science fiction' wasn't coined until the 1930s.
At one point Gil says that F. Scott Fitzgerald explained the concept of "cognitive dissonance" to him. But cognitive dissonance is a concept first defined in a theory of attitude change formulated by social psychologist Leon Festinger in the late 1950s.
The hotel physician called to attend John was going to listen to his heart, and he was using a Littmann stethoscope. He inserted it so that the slant of the earpieces was backwards. A person's ear canals slant toward the front and the earpieces were angled toward the rear.
The goof item below may give away important plot points.
Gil first meets Hemingway at the Parisian restaurant "Le Polidor". Upon exiting the restaurant he discovers he is back in 2010 when he finds a laundrette at the place of the restaurant. In the actual 2010 Paris, the restaurant still exists.