Factual error: According to the novel on which the movie was based, the "40" in the title refers to the number of players on a football team. But by the time the movie was made, football teams had 45 players. The coach even says Nick Nolte was just one of 45 players. So the title of the movie really makes no sense.
Factual error: During the period in which Apollo is trying to bait Rocky into a rematch, Rocky puts the TV on and sees a sports report in which Brent Musburger announces that the Los Angeles Rams defeated the Tampa Bay Buccaneers on a late field goal by Frank Corral. The movie takes late 1976-ish. The Rams did not play the Buccaneers in 1976, and Frank Corral did not join the Rams until 1978. The game in question occurred during the 1978 season.
Factual error: The toy horse on Alec's shelf is a 64 Black Foundation Stallion, available from Breyer between 1977-1987. But the film is set over thirty years earlier.
Factual error: When Dave is "true"ing his wheel, he adjusts one spoke with 3 full turns. That wheel would not be rideable after that much adjustment on one spoke.