Towards the end of the movie when the car "Yankee" is riding in, crests the hill approaching Chicago. A view of what is supposed to be Wrigley Field (home of the Chicago Cubs) is seen in the distance. Around the top of the stadium is what appears to be lighting framework. The events of the film take place during the 1932 World Series. Lights were not installed at Wrigley Field until 1988.
During a moment when Yankee brings lunch to his father at Yankee Stadium, the right-field light standards can be seen. Actually, Yankee Stadium didn't have lights installed until 1946 (14 years after the events in the movie).
In the 'newsreel' after the World Series game, the voice-over says that the Yankees scored seven runs in that inning, and that Babe Ruth drove in four. This is impossible because of simple math. Babe Ruth led off the inning with a strikeout - one out. The next batter also goes down - two outs. The kid (third batter of the inning) then gets an in-the-park home run - one run in and still two outs. Then let's assume that batters #4, 5, and 6 get singles without scoring. Every consecutive batter who follows must then drive in a run (no more outs to give). So if batters #7, 8, and 9 each drive in a run, the Yankees have already scored four runs in the inning by the time Ruth comes back up to bat. If he drives in four more, the Yankees will have scored eight in the inning, not seven as announced.
When Yankee and his dad are looking at Babe Ruth's bat in the Yankee's locker room, the dad says how Babe Ruth had it custom made 3 years ago, and Yankee replies how that was the first season Babe Ruth hit 50 home runs. Since the movie is set in 1932, it would mean that 1929 was Babe Ruth's first 50hr season. Babe had already had 4 50hr seasons-1920, 1921, 1927, 1928, and did not hit 50hr in 1929 at all.
Yankee is once seen holding a picture of Marty's dad. Marty is also seen taking the picture away from him. But If you look carefully, Marty's hand doesn't grip a hold of the picture. She just touches it and the picture then follows her hand until it goes off screen.
When Lefty finds the Babe Ruth's case that holds Darlin' he grabs it and places it on his lap, opening it only to find nothing. However, if you look the case is actually above his lap - it's not laying on anything, just sitting in mid-air.
At one of the last parts you see Mr. Cross pull a lever to rise the chair Yankee is sitting on. Then to rub everything in Yankee's face, he leans over closer to Yankee to talk in his ear. But it's completely visible that the lever he was pulling earlier is now going through his stomach.