When The Champ slaps T.J. he slaps him while standing up but, in the very next shot, he's kneeling down by T.J.
In the jail scene, there is a fan on a stand in the back, vacant corner of the cell area. It is motionless - blades are not turning. A few moments later, right before the Champ slaps T.J., the fan is now on - blades spinning - but there is nobody in the room near the fan who could have turned it on.
When Champ is badly beaten up in the ring near the end of the movie, he is almost unconscious. To try to make sure he is okay, Jackie asks Champ, "What day is it today?" Champ says, "Thursday, May 23rd." The film takes place in 1979. May 23rd, 1979 was actually a Wednesday.
Nighttime scenes were filmed during daylight hours using a filter to darken the scene. BUT using this technique left the sky bright and the sky at night is ALWAYS dark and black. Further, using this technique always leaves distant objects distinct with detail, where as if it really were night, they would have just disappeared into the background and shadows.
At the gym in the beginning of the film, Tex Cobb is being battered in a sparring match and his seconds call him Tommy. At the end of the film, Cobb is featured as Roland Bowers, Heavyweight Contender.