Factual error: When he bats, Jake uses a helmet with no earflap. In 1983, it was instituted that players must wear a helmet with at least one flap; however, it's possible that Jake is exempt from this rule under Major League Baseball's "grandfather clause," which allows any player who played before 1983 to continue using the flapless helmet. (01:34:40)
Factual error: In the ball park the sign for NBC says channel 4. In Cleveland, NBC was and still is on channel 3. (Filming took place at the old Milwaukee County Stadium, former home of the Braves and Brewers, hence the NBC, WTMJ channel 4 sign. Still a mistake, but there's the explanation.) (01:33:40)
Factual error: Shots of the first game or two have angles of the batters' shadows facing behind home plate (or in other words the sun is around left to center field in some shots). In major league games, that would not be a possibility due to baseball rules that the sun can not be in the batter's eyes.
Answer: He just shows up, uninvited. When he first arrives, they can't find his name on the list; he's later (comedically) removed from camp in the middle of the night when security carries him out on his bed (while commenting "This is the guy who wasn't invited to camp"). So, he's relying on his speed and charm to get him a spot on the team... which, of course, ultimately works.