When the coaches ask Sayers to room with Piccolo in 1965, they warn that people in cities like Atlanta, New Orleans, Houston and Miami won't take well to integrated roommates. Atlanta didn't join the NFL until 1966, New Orleans 1967, and Houston and Miami until the AFL/NFL merger in 1970. Miami wasn't even in the AFL until 1966.
The Bears are shown playing at Soldier Field in Chicago. While this was indeed the team's home stadium by the time of filming, Brian Piccolo's entire career had taken place while the team was still playing at Wrigley Field.
When the coach comes in the room to talk to Brian and Gayle to let Gayle know he will become number one full back, the boom mic's shadow shows above Gayle's head in the shot when the camera focuses on coach and Gayle.
When Brian and Gale are talking at the Sayers' staircase, Brian is standing at the base of the stairs holding a towel. After a quick shot of Gale, Brian is suddenly over by the wall with no towel in sight.
After Gale Sayers makes the announcement in the locker room about Brian Piccolo's illness, and the team visits him in the hospital room, which is supposed to be in Chicago, the exterior hospital establishing shot clearly shows the name of the hospital, the "New North Hospital of Los Angeles." Further, while Brian Piccolo did return to Chicago for the diagnoses, he ultimately transferred to a hospital in New York City, which is where he died.
When Gale Sayers suffers his knee injury, it's during his fourth year on the team, which was the 1968 NFL season. George Halas had retired as the Bears Head Coach after the 1967 season, although he was still serving as the Bears owner, and functionally as Bears general manager.
The character (and real life player) J.C. Caroline, portrayed by Bernie Casey, was the Bears team captain in the year that Brian Piccolo and Gayle Sayers joined the team. However, the film depicts Caroline being with the team through the 1965, 1966, 1967, 1968, and 1969 seasons, while he actually retired as a player after the 1965 season, after ten years with the Bears.
There is one moving camera shot on the football field with James Caan and Billy Dee Williams watching the action, but the view shows no players on the field. The crowd also roars as if a good play was made.