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. This term was not in wide use until the 1950s. Gil was referring to a quotation often attributed to Fitzgerald: "The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function."
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.
Over a bottle of red wine, Gil decides he just needs to share the truth with someone; so he proceeds to tell Dali and co. that he's from the 2000th millennium - obviously meaning to say the 2,000s', or the 21st century; but certainly not the 2,000th millennium.
Finding themselves in the 1890's, Adriana says to Gil: "it's the start of the Belle Époque". The Belle Époque is dated conventionally from the end of the Franco-Prussian War in 1871 to the outbreak of World War I in 1914.
Maxim's was founded in 1893 as Maxime et Georges, a bistro for coachmen. It wouldn't be until 1900 under Eugène Cornuché, who renamed it Maxim's when he took over in 1895 after original owner Maxime Gaillard died, that it became the high-brow, over-the-top Art Nouveau establishment seen in the film.
When the Doctor is checking John's Blood Pressure in the hotel room, you can see that he doesn't put the Blood Pressure Cuff on properly. Then, when the doctor is finished the Blood Pressure Cuff slides on John's arm. In reality it is put on tight initially and wouldn't slide when fully deflated.
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.