The American bar Max takes Jack to in Japan to meet other American players is actually a Sports Bar in Los Angeles. All of the patrons and bartenders/servers are American and all of the beer signs and posters are in English and if you look outside the window you can clearly see it's Los Angeles and not Japan.
When Jack and Uchiyama are drinking together, the amount in the bottle increases.
In the game where Elliot (Selleck) gets suspended, he starts a 3-6-3 double play where the batter runner is called safe at first, both the long shot (from left field) and the close up show that the umpire got the call wrong; but Elliot's mitt is positioned differently from shot to shot as is the first base umpire. In the long shot the umpire is about six feet from the base, but in the close shot the umpire is within four feet of the base.
During one of the games, Itoi is the pitcher and is wearing uniform #11 when he throws a pick-off throw to Jack at first base. When the shot changes and Jack catches the ball at first base, Itoi is warming up in the background wearing #11. Itoi can't be warming up if he is already on the mound in the game.
Even though this was the 7th break-a-ball, it came out on the same day as the 6th break a ball, but this break a ball came out first.
When Elliot is hit with a pitch in the final game, the trainer comes out and sprays the "freeze spray" on his uniform to lessen the pain. The spray is useless unless it's applied directly to the skin.
During the Dragons season ending series, Jack is scouted, and Max is signed to finish the year with the LA Dodgers. Japan's baseball regular season ends a week or two after the Major League Baseball regular season ends. If Jack or Max had signed a contract with a Major League team at that time, they wouldn't be eligible to play until the next season.
When Doc tells Jack about the Dodgers wanting to hire him, Doc mentions the Dodgers begin a series with Atlanta on Saturday. No regular season series begins on Saturday as a series will usually begin on Friday or Thursday if it's a four game set.
When Jack calls his agent in the U.S., it is day in both places.
When Jack is called out for stepping on the plate in the final game, the manager comes out and twice bumps the umpire which should have immediately resulted in an ejection.
In the scenes where someone is driving, the steering wheel is on the left side. Japan drives on the left side, so the steering wheel should be on the right side.
All of the Japanese scoreboards in the movie show the batting order using the numbers based on the players' positions in standard baseball scoring, i.e. 1=pitcher, 2=catcher, 3=1st base, and so on. The batting orders show Jack Elliot is the clean-up batter, which is fine. The Japanese use lights above the numbers to indicate who is up to bat. Even when Jack is up to bat, the clean-up position never gets lit. Mostly it's the second batter. Once, in an an away game, the other team has a batter lit up, even though the Dragons are at bat.
At the end of the final game, Jack bunts. The ball goes towards the infield between the mound and 1st base. However, the 1st baseman is missing. He then is shown behind the pitcher and Jack, who are both running to 1st base. This is not possible as the 1st baseman had previously been at 1st base. He can't be behind the pitcher on this play. Either he should be at 1st or he should be fielding the ball to tag Jack out.
When Jack calls Doc on the phone at his office in New York and asks Doc to get him out of Japan, it is daytime in Japan. We see that it is also daytime in New York. Since Japan is 13 hours ahead of New York, and assuming a 9-to-5 work day in New York, it could never be daytime in those two places at the same time, at a time when anyone would be doing business in New York.
In the locker room when "The Chief" (Uchiyama) is fining Jack for disrespect of equipment, Jack hands him an additional 10,000 Yen. The Chief asks in Japanese (and Yoji translates into English) "What is the second one for?" Jack replies, "That's for the next time." Yoji doesn't translate Jacks answer into Japanese, yet The Chief asks (again, in Japanese and Yoji translates) "He wonders when the next time will be." He inadvertently reveals that he understands/speaks English, long before when he reveals it at the grandparents' home.