Although the film is set in 1958, the garage scene uses a 1961 re-recorded version of Rum And Coca Cola by The Andrews Sisters. This version was recorded for Dot Records, two years after the movie's setting.
The bullet hole in the windshield of Jack's Cadillac has long cracks radiating from it in all the scenes in the country; but, when he returns to Havana, the cracks are gone and only the bullet hole is there.
At the end of the movie, Roberta is standing up at the table where Jack is sitting and you can see his right shirt sleeve rolled way up revealing a bandage strip on his outer right forearm where he had the diamond removed. In the next and subsequent shots, the bandage is not shown until Roberta rolls up his sleeve to reveal the bandage.
In the final conversation between Jack Weil and Bobby Duran, Jack refers to the Butterfly Effect as if it was already theorized and calculated. This is supposed to be the following days after the Cuban Revolution blasts, in early 1959. Although the idea of the ripple effect exists since before, the way Jack refers to it should only be possible to know after that, as related to the work of Edward Lorenz. This mathematician and meteorologist wrote a paper for the New York Academy of Sciences in 1963 noting "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever." In later speeches and papers, Lorenz used the more poetic word butterfly.
According to the movie, the final scene takes place in 1963; so, the Santo Domingo reference would be correct.
The big concrete symbol on the entrance of the palace where the big New Year's Party occurs is in fact the Seal of the Dominican Republic, which doubled for Cuba in the movie.
There was no Santo Domingo in 1959. The capital city of the Dominican Republic at the time was Ciudad Trujillo. It became Santo Domingo in 1961.