When Belinda is confronting Ali about his relationship with Veronica in Zaire, there are Cell Phone antennas clearly visible on the rooftop of next door building. Commercial Cell Phone Networks were 15 years away from being developed in 1974.
Around 25:30 into the movie, Cassius Clay celebrates his victory over Sonny Liston by leaning over the ropes at the side of the ring, arms raised and yelling at the crowd. He has his mouth guard in and clearly visible from the side of his head. The film quickly cuts to a straight on shot, the mouth guard has disappeared and we see his teeth, his arms still raised above his head.
The officer at the induction center wears the belt of an Army officer (black), indicating that he is an Army captain, yet he wears his rank like a Naval or Coast Guard lieutenant (with the bars' center line bisecting the collar angle, and lacking branch insignia on his left collar).
Early reference to Ali's argument and Angelos not being in Ali's corner were errors. It was Belinda who confronted Ali about Veronica Porche.. And it was the Jimmy Ellis fight the Dundee didn't assist Ali. Dundee trained both as Ellis was Ali's sparring partner.
The argument Ali and his wife Sonji have over Ali's seeing Veronica Porche did not happen before the Ali/Foreman fight, but instead happened before the 3rd Ali/Frazier fight, "The Thrilla in in Manila", in 1975.
In the early '60s section of the film Clay refers to a member of the Beatles ('John Lennon' we presume) as "the one with the glasses". Lennon seldom wore his glasses in public (though there are a few studio photos), and was certainly not famous for them, until 1967. It is possible however that Lennon would have been wearing his thick-rimmed black glasses when the Beatles met Clay during their first visit to the U.S. in February 1964, then removed them for the publicity shots taken during that visit.
When Martin Luther King is shot, while trying to recreate the famous photograph of bystanders pointing in the direction of the shot while crouching over King's body, the sign of the famous "Knickerbocker" building in Hollywood is visible. King was shot in Memphis.