Other mistake: Near the end of the movie, Ricky Vaughn strikes out the Yankees' best player, ending the inning. As they walk off the field, the Yankees' Third Base coach is still in the coaches' box. He has no need to be, he should be off the field.
Continuity mistake: In the top of the ninth, as Harris struggles with his control a shot of the scoreboard shows both teams have 2 runs, 7 hits and no errors. Harris then walks the next batter to load the bases, and Vaughn is brought in to face Heywood, whom he strikes out. Thus the Yankees should still have 7 hits heading into the bottom of the ninth. Yet when the scoreboard is shown as the Duke comes in shows the Yankees with 9 hits. This means they somehow picked up 2 hits in between the half-inning, which is impossible. The only way to gain hits like that is if the scorekeeper changed two errors from earlier in the game into hits, but the scoreboard indicated there no errors were ever made in the game. (01:27:20 - 01:33:30)
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.