During the third inning when Billy throws three pitches, all of which are preceded by the announcer saying 'Strike Three,' the same player's picture can be seen on the screen in deep right center field in the background.
Chapel mentions on the plane that he'll be pitching tomorrow and the radio broadcast mentions on game day that it is the second to last day of the season. It is highly unlikely, if not impossible, that a pair of Major League teams would end the season on a 2 game series.
At one point while announcing the game, Vin Scully describes calling Don Larsen's perfect game in the 1956 World Series, then states that "I never thought I'd be able to see another one." In real life, Scully had called additional perfect games in 1965 (by Sandy Koufax) and 1991 (by Dennis Martinez).
At the end of the third inning, the announcer says that Billy
strikes out the side and now has five strikeouts. Billy strikes out the second batter and third batter in the first inning, and strikes out the first batter (fourth batter in the lineup) at the start of the second inning. During the eighth inning, it's revealed that the sixth batter in the lineup struck out twice previously, which means he struck out back in the second inning. If Billy struck out the side in the third inning, he should have at least seven strikeouts by the end of the third inning, not five.
At the end of the third inning, the last Yankee hitter is walking up the first baseline complaining loudly about a called third strike. We know he is the sixth batter because he bats third in the eighth inning (and if it's in the midst of a perfect game, he's batting sixth in the lineup). At the end of the third inning, it'd be the ninth batter that had just struck out, not the sixth batter.
As the third inning ends the TV network scoreboard graphic indicates that neither team has any hits, runs or errors. Moments later a shot of the Yankee Stadium scoreboard indicates the same thing. However, when the fourth inning starts TV announcer Vin Scully states that the Yankee pitcher has allowed two hits.
When Mickey Hart saves the would-be Davis Birch home run in the 8th inning, the initial close-up shot sees the hands of fans vying for the ball, but when shown from distance Hart makes the catch on a part of the wall that is nowhere near any spectators.
During the first overhead shot of Yankee Stadium, the left field upper deck is completely empty. Later that section is full from a field shot. During a later overhead shot, that section is empty again.
Billy Chapel warms up in the bullpen prior to his final game wearing the 1997 uniform of the Detroit Tigers. However, when he takes the mound, and for the balance of the movie, he's wearing the 1998 Tigers uniform. The difference is a prominent quarter-inch navy blue piping on the front of the jersey (around the collar and parallel to the buttons).
When Jane arrives at Winter training, she tells Billy about her flight to Lauderdale. The Detroit Tigers Winter Training is in Lakeland, FL, near Tampa. She would have flown into TPA, Tampa International Airport.
Baseball has a rule saying that any player who has been in the MLB for 10 or more years, and has played the last 5 or more consecutively with the same team has a full no-trade clause. Having played the last 19 for the Tigers, so they could not have traded Kevin Costner's character without his permission to do so.
When Gus Sinsky is at bat and gets his double, one shot shows the sun in front of him. With the orientation of Yankee Stadium, the only time the sun could be in that position is in the morning, but the game time is late afternoon/evening.
Billy Chapel would not be able to be traded to the Giants. He could invoke the 5/10 Rule whereby players who have been with a club for at least 5 consecutive years and have been a major league player for at least 10 years cannot be traded without their consent. However it is mentioned that he will be a free agent at the end of the year, at which time the new ownership can simply choose not to re-sign him to a contract with the Tigers.
At Boston's Fenway Park, a batted ball could not bounce off Mickey Hart's head upwards into the stands for a home run. Mickey plays Right Field for the Tigers, and Boston'd Right Field Stands are almost right at field level. The Right Field 'wall' is about waist level for most outfielders.
The shirt he has on under his jersey had the "home" white "D", instead of the road colors - orange "D". However, there are no regulations as to what a player wears UNDER his jersey/uniform. Billy might simply have chosen to wear a home t-shirt, for any number of reasons.
In the ninth inning of Billy's perfect game, a foul ball is hit by a Yankee into the stands. The negative is flipped - a fan's shirt has the name "Jeter" spelled backwards along with his uniform number "2".
In the beginning of the movie, one of the newspaper's headlines states, "Chapel Pitches Lincoln To Title For Second Straight Year." All of the bold print is about Chapel's high school career. However, all of the print is concerning a game the previous night between Detroit and New York in which Billy Chapel pitched.