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: In the scene where Ali arrives in Zaire, as he is walking across the airport tarmac you can see a white Land Rover Discovery behind the crowds. These weren't made until the late 1980s.
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.
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.
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.
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.