The baseball cards of Roy Hobbs rolling off the printing press are clearly meant to be those manufactured by the Playball Company (which produced cards from 1939-41). And though the film takes place during the 1939 season, the card style corresponded to Playball's 1941 set.
In the scene depicting the team on a passenger train streaking across country as the Knights make their "run" at the pennant, the drumhead on the observation car says "Super Chief". This would make it a Santa Fe high-speed train running daily between Chicago and Los Angeles. Since the movie is set in 1939, they would not be riding that train because there were no major league baseball teams west of St. Louis in those days.
Several news photographers shooting with 4x5 Graphic press cameras are using Pacemaker models (aluminum lens boards) that weren't introduced until the early '50s. The Graphics with dark wood lens boards are in period.
In the at-bat when Roy Hobbs breaks the clock, before he sees the woman from his past, strike two is a swing and a miss in the audio, but visually, Roy Hobbs connects with the ball. The hit ball can be seen streaking across the top of the picture.
During the game in which Roy Hobbs bats for the first time and knocks the cover off the ball, there are two different home-plate umpires: The ump who comes to the dugout to talk to Pop Fisher is not the same ump who later calls a strike on Hobbs and then stares him down.
In the game where Hobbs breaks the Wrigley Field clock, his homer ends the game, as everyone in the stands begins to leave and Hobbs gets mobbed by the press. But since the Knights were the visitors, the Cubs get to bat last.
In the final game, Roy Hobbs strikes out in his first two plate appearances, then hits the game-winning home run in his third. Every spot in the order will come up at least three times in a 9-inning game, meaning that Roy couldn't have been up only twice before the home run.
After Roy starts dating Memo, the Knights start losing, and there's a newspaper headline that reads "Cold Knights in August." When they start winning again, under the headline "Knights in 3rd" is a dateline of "Boston, July 8."
After Hobbs splits "Wonderboy", he tells the bat boy to pick him a winner. The bat boy gives him a bat called "Savoy Special". When Hobbs hits the game winning home run, supposedly with "Savoy Special" you can see the lightning bolt from "Wonderboy" in his hands.
At the beginning of the movie when Hobbs is waiting for the train to take him to New York, he only has one bag. The trombone case in which he carries Wonderboy is not there, but when he arrives at Knights Field he is carrying the case. [This is explained/corrected in the Director's Cut, which re-edits the film's opening into a flashback structure, showing Roy returning to his now-dilapidated childhood farmhouse to retrieve the bat.]
After Bump's funeral (and after the lightning patch has been added to the uniforms) there is a batting practice scene where Bump (#7) is seen wandering around behind the backstop. The lightning patches are also missing. The scene is combined with the managers trying to guess the names of songs.
When Max Mercy is umpiring the match-up between Hobbs and the Whammer at the carnival, he takes several steps back after the first pitch. Before the next pitch, he is directly behind the catcher in a crouch, and then as Hobbs pitches the ball, he is once again several steps behind the catcher.
In the game against the Phillies when Bailey runs into the centerfielder causing the error, Roy is shown in the dugout with no hat on, leaning over. Immediately after that cut, he is shown sitting up with his hat on.
When Pop benches Bump Bailey and sends Roy up to bat for the first time (at around 38 minutes), Bump is walking up the steps of the dugout to the field. When Pop stops him, Bump is clearly holding a bat, since he raises it to his left shoulder as shown from behind. After the quick cut to the front view of the dugout, when Pop is still talking to him, Bump's bat has disappeared from his hand.
During his first at bat where he knocks the cover off the ball, as Roy is sliding into the base and the Knights are yelling for him to slide, Roy can also be seen in the dugout. Bump Bailey should be there in that scene, but he's not in the dugout.
When Hobbs hits four home runs in Chicago, the announcer states on two occasions that it is the bottom of the inning when Hobbs bats. The NY Knights, as the visiting team, would have batted in the top of each inning.
When there are two outs in the final inning of the final game, there are runners on first and third base. The pitcher then throws the next pitch from a full windup, instead of the stretch position. The runner on first never advances as he certainly would have on a pitcher's full windup.
When years later Hobbs makes just "one" pitch at the end of practice, ...the ball zooms across the plate and lodges into the net behind. You can clearly see a string attached to the ball as it lodges into the net.
The bullet the Doctor hands Roy in the hospital is pristine. If it were shot through the barrel of a gun, it would show markings due to the rifling of the barrel. It would also be highly unlikely that the lead bullet would be completely undeformed if Roy were shot with it...Maybe if he swallowed it, but not if he got shot with it.
When Iris is reading the paper about Roy's slump, none of the headlines actually match the story being written about and seem totally unrelated to the headline. One example where the headline reads, "Knights at Wrigley Today," is actually about a polo tournament in Houston Texas.
In one of the last scenes, right after Hobbs returns the $20,000 bribe money, Pop is seen crossing off Hobbs name from the line-up card, assuming he can't play in the final playoff game because of his injury. But the line-up card is numbered wrong: Hobbs is #3 (being crossed out), and the numbers continue: 4, 5, 7, 6, 8, 9.
If you read the newspaper article that is shown in the coffee shop after Hobbs's first at bat, it states that he hit a stand up triple and put The Knights ahead of The Phillies 4-3. But in the actual scene, Hobbs not only slides into third base, The Knights actually won 5-4.