In the final game scene, (just before the World Series), a left-handed batter wearing number 43 runs to first base. His chest was not visible, until he nears the base. Instead of wearing the St Louis jersey, the logo on his chest is that of the Chicago Cubs.
Objects on the dresser change as Monk and Vernon chat.
Deborah's sash changes as she receives the package.
The position of the newspaper on the bed as Monk brushes his hair.
The same stadium scenery is used to represent several teams and games.
When in the lab as the professor tries to hit the baseball hanging by the string, it's obvious that the string is being jerked up. If the ball moved up on its own, the string would go limp since it can only resist tension, not compression.
Kelly's pitch violates the laws of physics. Assuming arguendo that a chemical exists that avoids wood, when a ball with that substance on it approaches the plate and the batter swings, the ball would change its trajectory either up or down to avoid the wood and would then continue on that new path. It would never "jump over" a swinging bat, then go back to its original trajectory.
When he is pitching to Schmidt at the campus diamond, Professor Simpson's shadow is visible on the backdrop representing the field. The 5:00 time is/was World Time.
When Vernon asked his two students, (the hot-footer & the recipient) to meet him on the baseball field at 5:00 A. M. the next day, no where in the United States, is it lit, or even dawn, at 5:00 A. M. in the spring. Perhaps, Vernon's 5 o'clock remark, was referring to another time zone, like Pacific. When it is 5:00 A. M. Pacific, it is 7:00 A. M. Central Standard Time. (Apparently, the 5:00 Time, is/was World Time).
If the Professor's magical chemical really repelled wood, then when swinging the bat at the ball it would be pushed away from the batter and cause a foul or in field ball, rather than just hop over the bat.
In the first baseball game sequence, they start outside the St. Louis stadium. The (stock) game footage they use immediately thereafter is obviously Chicago's Wrigley Field. The movie footage is then inside the stadium in St. Louis again.
As Vernon returns by train from St. Louis to the university, the conductor rouses him and tells Vernon this is his stop. Columbia, MO, location of the University of Missouri, had no direct train service from St. Louis. Vernon would have to get off the train from St. Louis at Centralia, MO to connect with a branch line shuttle train to Columbia. The branch line was 21 miles long and Columbia was the last and only stop. The conductor would see no need to alert a passenger as the train pulled in.
After class, Debbie tells the clearly distracted Vernon, who was surreptitiously listening to a ballgame during class, he seemed to be "a million miles away." Vernon replies, "No, only 68." The distance from Sportsman's Park, then home of the St. Louis Cardinals and Browns, was 115 miles.
Kelly's pitch takes a "hop" only when a batter swings at a pitch. If the batter doesn't swing, its just a medium straight fast ball. Sooner or later somebody would notice that the pitches swerve only when swung at, and would start taking a look at the ball and discover that it had been doctored.
Kelly pitches from a windup with a runner on base instead of the stretch which allows him to check the runner's lead. In a real game the runner would easily steal the next base at each occurrence of this type of windup let alone the double pump Kelly uses.