As Dink plays on the balcony awaiting his meeting with Linda, he steals chewing gum and candy for himself off of a table on the balcony. He then steals the contents of a box of cigarettes, saying that he'll "bring some home for the Champ", and stuffs them into his right jacket pocket. However, during the ride home, Andy reaches into Dink's right jacket pocket and finds cigars rather than the cigarettes which we clearly saw Dink steal.
During the fight, The Champ sustains a cut above his left eye, but when he goes back to his corner it is gone. The cut comes back when the fighting resumes and stays for the duration of the film.
When the Champ Andy Purcell punches the wall in the locker room, the wall has blood on it before Andy strikes it, and the bloody area gets larger as Andy continues punching and his own fist gets bloody.
From 4:36 to 4:43, camera shadow in the tracking shot.
From 25:57 to 26:15, camera shadow in tracking shot.