Factual error: When Kevin Costner says that if the pitcher starts him out with a curve-ball he is taking him downtown, he strides to the plate and pounds a homer over the left field wall. However, the shot that shows the ball actually flying over the wall shows the distance at 410 feet. No minor league or even major league ball park is 410 to left field, indicating that the shot was actually taken in right center, no where near where Costner's ball actually went out.
Suggested correction: I have played at old minor league stadiums with much larger dimensions. One must check the schedule of the Durham Bulls and find dimensions prior to making this claim.
Other mistake: In the beginning of the movie, the catcher is in the dugout eating a hotdog in front of his manager. Pretty gutsy (or stupid) thing to do, since no manager would ever allow his players to eat something like that right before or during a game.
Suggested correction: Defying a custom isn't a movie error. Also, considering that dietary restrictions for a Single-A ballclub in 1987 were likely far looser than today, it's possible the manager doesn't actually care.