Audio problem: When Henry is at bat, his mother is berating the pitcher. She starts saying you stupid mother... and it cuts to Gary Busey completing the sentence. He says "God damn," but his mouth doesn't match. Chances are he said the f-word but it was changed in post for ratings issues.
Continuity mistake: While flying on the road trip, the interior shots show a widebody aircraft with twin aisles. The exterior shots show the much smaller 727, which only has a single aisle.
Factual error: The application of the hidden ball trick by the Cubs at the end is illegal. MLB rule 8.05i states a balk is awarded if "The pitcher, without having the ball, stands on or astride the pitcher's plate." Also play doesn't resume after a time-out until the pitcher is on the rubber. AND the only way to pull the hidden-ball trick is if the pitcher is off the mound entirely (check out any of the MLB examples over the last years to see how to legally do it). The rules are written specifically to prevent this type of play. As far as any claim that Henry did not call an "official" time-out, the vast majority of MLB rules regarding timeouts don't require a vocal request. Hitters raising one hand, pitching coaches or managers simply setting foot on the field, all signal timeouts. Calling the entire team in to the pitching mound indicated a cessation in play, which means play cannot resume until Henry toes the rubber and assumes a pitching stance (which he does). Since he transferred the ball to the first baseman while play was halted it is a balk.
Continuity mistake: Towards the middle of the movie, they show the Cubs shortstop make a play. The stands behind him are completely empty, however, just a few scenes later they are filled with people.
Continuity mistake: When the Cubs are in L. A. Playing the Dodgers, Henry walks when he goes up to bat and when he gets to first base, the pitcher attempts to pick him off. Henry slides back headfirst safely. He gets some dirt on his uniform. They cut to the pitcher and then cut back to Henry, who now has less dirt on his uniform than he did before.
Continuity mistake: When Hedo comes in for the final at-bat, he's a right-handed hitter as always (and Henry's a right-handed pitcher so there's no switch-hitter issue). However, the shot right after shows a hitter digging in on the left side of the plate, then shifts back to a view of Hedo on the right side. The direction of the tip of the plate, which is a pentagram, makes it obvious.
Factual error: It is announced that Henry's first game is on August 14. But in the next scene his friends are seen in a crowded school cafeteria. It's summer which means school wouldn't be in session. If it's summer school then there wouldn't be that many kids in the cafeteria and I doubt the girl Henry likes would be attending summer school.