Aristotle Onassis and Maria Callas met for the first time on a party in Venice, not on a cruise ship.
The famous headline "The Golden Greek" was released in 1948, two years after his marriage with Tina Livanos. In the movie he meets Tina after being nicknamed "The Golden Greek".
The first time Jacqueline Kennedy referred to Kennedy's administration as "Camelot" was one week after JFK's assimilation. In the movie this happened before the birth and death of their son Patrick.
Onassis gained ownership of Olympic Airways in 1957, around the time he met Maria Carras, while in the movie it was shortly after the to Tina Livanos.
The real Aristotle Onassis had the size of 5'05'' (1,65) while Raul Julia was 6'02'' (1,87m).
Onassis first became the target of the FBI before 1954, not in the 1960s as shown in the movie.
During the marathon race scene at the beginning of the movie a modern flag of Greece is shown, which wasn't introduced until 1970. The scene however is set around in 1922, since Onassis referred to the Greco-Turkish War and the Turkish occupation of Smyrna was mentioned. Later, on one of Onassis' ships, also the modern flag of Greece is shown, despite the scene is set in the mid-60s during the LBJ-administration.
When talking to the camera Athina Livanos said that when she and Onassis were married in the age of 17 "Ari (Onassis) was 46". However Aristotle Onassis was 40 when they got married. The year however was 1946.