The issue with the player with the fake birth certificate really happened. Danny Almonte, originally from the Dominican Republic, playing for a US team from New York was found to be too old. He was actually 14, not 12, the cut-off age. He had a forged birth certificate. His team had won their regional competition and were eliminated in the semifinals of the Little League World Series but, as a result of the scandal, the entire team was disqualified, had their records erased and the coach banned for life from Little League baseball.
The stadium built for the final game features architectural details borrowed from several Major League parks: Yankee Stadium since 70s (the "wedding-cake" trim on top of the bleachers' wall), Wrigley Field (the brick-and-ivy fences), Fenway Park (the Green Monster fence) and Chase Field (the pool area behind right field).
After their first game, David Spade walks out of the field with the other two wearing his sunglasses. This is the only scene where "Richie" wears sunglasses, because the director didn't allow the character to wear them. However, in this scene, he had forgotten to take his glasses off after being backstage and the director thought that the take was so good, he didn't bother re-doing the take.