An hour into the film, Ed gets into a cab. When he closes the door you can clearly see a NO SMOKING symbol on the car's window, a symbol that was not used until decades later when smoking bans came into effect.
When a gramophone is shown playing 'Non, Je Ne Regrette Rien' by Edith Piaf, a little over 35 minutes into the movie, a close-up of the record player reveals Russian characters along with numbers above the stylus (the Cyrillic equivalent of "GZM, 205D").
The Lockheed Constellation had four huge 3,500 HP Pratt & Whitney Turbo Compound engines. I don't think the engine sound dubbed into the stock footage of the TWA Constellation landing is correct. It is not the deep growl that I remember from these classic airliners.
While in Cuba before the successful 1959 revolution, Hemingway is quoted as saying "ever since J.Edgar Hoover died" they were trying to "get him". Hoover died in 1972, much later than the Cuban Revolution.