Factual error: The poem Ali quotes in the movie before the Frazier fight, "Ali comes out to meet Frazier, Frazier starts to retreat, If he goes back any further, He'll end up in a ringside seat..." was in fact the poem he used before the first Liston fight and began, "Clay comes out to meet Liston, Liston starts to retreat..." and ends with the lines, "Never did they think, When they laid down their money, That they would witness, The total eclipse of the Sonny". Poor effort.
Factual error: When the ring announcer introduces Ali and Foreman to the crowd before the "Rumble In The Jungle", you do not have to speak fluent French (I don't, and I noticed it) to hear that he introduces ALI as fighting out of the BLUE corner and FOREMAN as fighting out of the RED corner. In the actual fight, as in the film, it was ALI who occupied the RED corner and FOREMAN who occupied the BLUE corner.
Continuity mistake: In the scene with Ali in training camp preparing for his first fight with Joe Frazier, he receives a call from Howard Cosell informing him that the Supreme Court had ruled in his favor regarding his refusal to enter the Vietnam draft. Ali could not have received this call while training for this fight with Frazier. The fight with Frazier took place on March 8, 1971. The Supreme Court did not even hear the case until April 19 and did not rule on it until June 28, 1971. In fact, one of the reasons the fight was scheduled in March and not later that year had to do with the pending Supreme Court case and the concerns that Ali would lose and sentenced to jail, which would have prevented the fight from happening.
Factual error: When Ali's second wife Belinda flies out to Zaire prior to his fight with George Foreman to confront him about his affair with Veronica Porshe (who later became his third wife). It's true that Ali first noticed Veronica in Zaire when she went along as a show girl, but Ali and Belinda's argument actually happened in Manilla, Phillipines before Ali's third fight with Joe Frazier a year later after he had taken Veronica to visit President Marcos in full view of the press. Belinda flew to the Philipines, had her argument, then flew straight back to the US.
Factual error: This may be more of an issue of product placement, rather than a mistake. However, for a period piece that encompansses part of the 60's and 70's, the Nikon cameras that some of the "press" uses in crowd scenes are clearly present day ones. The producers even mix and match, with some "press" using cameras from that period, as well as some using modern day ones.
Continuity mistake: When Malcom X visits Ali in his hotel room to tell him that he's been suspended from the Muslim Order, Ali is seen sitting down twice.
Factual error: In the film, the canvas of the ring on which Ali fights George Foreman is plain white. The canvas was, of course, a distinctive blue in Zaire.
Continuity mistake: When Ali is driving and hears of Malcom X's death, he pulls over. There are back and forth shots of him from inside the car and from the front of the car. The shots from inside the car show sunlight on his face. The shots from outside the car show him in the shadow.
Factual error: Ali argues with his wife in their hotel room in Zaire, prior to the Rumble in the Jungle. A modern cellular antenna is seen through the window on a rooftop across the street.