Audio problem: Towards the end when Rubin Carter is in court, there are numerous occasions when you can hear the courtroom observers talking and whispering to each other. In the camera shots of the observers, there is not one person that is visibly talking.
Other mistake: When Lesra is on the bus visiting Rubin for the first time you see a shot of him through the window. The bus is rocking and you can hear the engine (as though the bus is moving) but the reflection in the window remains the same.
In the film, Hurricane Carter is shown as having published a book called "The Sixteenth Round." This book, as well as parts of Sam Chaiton's (played in the film by Liev Schreiber) book "Lazarus and the Hurricane," is what the film is adapted from.