When Henry arrives to his first game for the Cubs, he arrives at a "player's entrance." There is no such entrance, only a player's only parking lot with a small door that leads to the main concourse before going into the locker room.
When Henry, his mom and Chet escape from the mob of reporters in the airport, Henry changes the station on the radio after he is ridiculed for turning that kind of music on (romantic). Right before the scene cut, the sound is of an analog radio's tuning knob being moved up or down (01:00:57 to 01:01:00), with several stations and static all combined into one sound. However, this would not be possible because the radio in the limo has digital tuning (shown at 01:00:32).
When Henry throws the opposing Home Run back to home plate from the bleachers (at around 42 mins), the runner is deemed "safe" by the umpire. Though the ball had been hit as a home run and there would be no reason for a player to slide into home, this would have more than likely been the first time that the umpire and the player who hit the home run had experienced this, and therefore had no idea what to do.
When Henry is doing commentary for his imaginary baseball game in the laundry room, he states (at around 4 mins) that it is a "full count" (by definition, three balls and two strikes) before he throws the pitch. However, when he pitches into the laundry machine he cries out, "Strike ONE!" (at around 11 mins).
To get the third out of Henry's second save, he pitched a strikeout on three swinging strikes (40:30 to 45:30). The umpire called the batter out. In baseball, an umpire does not call strikes unless the batter does not swing (looking). This called strike was unnecessary and may have been done for added dramatic effect.
When Henry first gets his cast on (at around 6 mins), it is shown as having a diagonal bar connecting about halfway between his shoulder and his elbow to hold his arm up. Never again do we see this bar, and none of Henry's shirts seem to be large enough to accommodate it. In addition, he hangs his arm fully outside the window of the van (at around 24 mins), something that would not be possible with that bar in place.
The movie begins with the first game of the season (01:38). When a ball is hit into the outfield, a player runs to the wall in center field, which shows the signature ivy (3:42-3:47). The ivy is not in full bloom until much later in the season.
After Henry throws the ball back from the bleachers, general manager Fisher sends his assistant to find out who threw the ball. When he returns to the owner's box (at around 40 mins) you can clearly see that there are no fans in the bleachers. This contradicts the numerous fans that are in the bleachers when Henry throws the ball back in the scene before.
Henry attends the Cubs game August 11th at which point the season has been considered disappointing (at 45:58, after Henry saves his second game, the announcer says he has extended the Cubs to their longest winning streak of the season: two). After Henry's arrival and in 3 weeks there is all of a sudden "pennant fever" and the Cubs win the division. Seems too little too late.
Henry's jersey number is #1. However, at the last game when Henry is throwing several pitches striking out the other team, there is a quick shots showing a different pitcher throwing wearing jersey #32 (at around 1h 25 mins) which is Chet 'Rocket' Steadman's number.
When Henry arrives to his first game for the Cubs, Jack can be seen (in a long shot from 24:14 to 24:23) running several yards behind trying to catch up. In the next shot, he is standing directly behind Henry (in a close-up at 24:23 with only Jack's green shirt visible behind Henry), breathing normally.
In the last game in which the Cubs beat the Mets, 10 innings are shown being played instead of 9. The Rocket pitches 6 solid innings, as said by the manager after he threw out his arm, and Henry comes in and throws three innings worth of outs during the shots following him coming in, then pitches a fourth inning once he fell on his arm.
When Henry is called from the dugout for the first time, the "Rocket" is pitching and everyone seems to act like he had a horrible game. However, after the game, John Candy, the announcer, says that Henry got the save with a 5-4 win. Henry gave up a Home Run, so the worst that the "Rocket" could have done was throw 7 innings giving up only 3 runs, which is pretty good by anyone's standards.
In the final game, everyone is saying that this is the Cubs last inning to keep their 2-1 lead over the Mets. While this is true, the home team always has the bottom of the inning; had Heddo hit the home run and the next batter got out, it would've been the bottom of the ninth, not the end of the game.
After Henry falls on his arm, he executes the hidden ball trick. First of all, after a time out the umpire does not put the ball in play until after the pitcher gets on the pitching rubber. Secondly, if the umpire does put the ball in play, and the pitcher is on the dirt without the ball, the play is ruled a balk and runners advance. There is no way a runner can get called out.
When Henry sits on the bench for his first game, he is told to move with the explanation that pitchers sit at the end of the bench. However, at Wrigley Field the bullpen is out in the open in foul territory.
In the movie they make a big deal out of Henry needing to bat against the Dodgers. The Cubs themselves are in the National League and pitchers are able to bat in any game. However, it is rare for relief pitchers to have plate appearances, so Henry obviously did not have ample batting experience and perhaps the Dodgers may have been a particularly fearful opponent to have your first plate appearance against.
In the first game that Henry plays, it is clear that the game is sold out. However, when Henry is cheering on the Rocket from the dugout, the hitter gets a hit up the middle (at around 24 mins), and you can clearly see there is no one in the outfield bleachers. There are no empty bleachers in the wide screen version. At 29:25 in the full screen version four to seven rows of empty bleachers can be seen in three columns at the top of the frame, but these are cropped out in the wide screen version.
In school the day after the bad little league play/home opener it would be April in Chicago and Becky is wearing a tank top (at around 2 mins). Also, the boat ride with Becky supposedly would have been mid-September, rather late in the season to be at the beach in Chicago and again wearing the tank top (01:13:43).
In the last game that Henry plays for the Cubs, the Cubs rally and score in their half of the fourth inning. In that inning a Cub player hits the ball and the announcer says "And Mullens lashes one into left!" when the brief close-up shot of the batter hitting the ball clearly shows (one frame at 01:19:33) the ball being hit to the right. The subsequent, longer shot shows the ball going near the third base line.