In the newsreel that opens the movie, Leon Carter's team is identified as the Baltimore Elite ("e-leet") Giants. A team by that name existed, but its name was pronounced "e-light."
In the 9th inning of the game to decide the fate of the All-Stars, Leon Carter (James Earl Jones) hits a 3-run homer to win the game 3-2. Unfortunately, he stepped out of the batter's box and over the top of home plate to hit the ball because the other team was trying to intentionally walk him. Rule 6.06(a) states that a batter is out if he hits a ball with one or both feet on the ground entirely outside the batter's box. Leon should be out and the score should revert to 2-0.
When Leon breaks through the lid of the casket, you can see that is made of Styrofoam, and clearly not of wood or metal.
While examples of racism and racial name-calling are seen, there's no evidence of institutional segregation in food service, accommodations or otherwise.
A modern scooter and a modern convertible are visible in the distance during the fight between Bingo and Leon.