Deliberate mistake: To make Jim Braddock look more heroic, Max Baer is portrayed as being very mean and hateful. In fact, the real Max Baer was an extremely pleasant man who was devastated when Frankie Campbell died after fighting him. Many boxing historians and sportswriters have complained about this inaccurate depiction of Baer.wizard_of_gore
Continuity mistake: When Mae is at the sink washing dishes and, behind her, Braddock is teaching his kids how to box, Mae turns around and emotionally yells, "No boxing in the house!", the strap on the apron she is wearing is twisted. They cut away and in the next shot the strap is no longer twisted.
Other mistake: During the Baer and Braddock fight, when the camera angle is from far away, you can see that Braddock is not actually connecting with his punches on Baer. Yet Baer still reacts like he's been hit. This also true with Baer hitting Braddock when the camera is showing the fight from far away in the stands.
Mae Braddock: Maybe I understand, some, about having to fight. So you just remember who you are... you're the Bulldog of Bergen, and the Pride of New Jersey, you're everybody's hope, and the kids' hero, and you are the champion of my heart, James J. Braddock.