Factual error: When Hooker gets caught in the phone booth by Schneider, the very last shot has Hooker running down a street with a row of cars contemporary to the period parked on the left. If you look just beyond the 'prop' cars, you can see modern cars parked.
Other mistake: The reporting of the horse race used to sting Doyle Lonnegan stops as soon as the fake FBI agents raid the bookmakers. J J Singleton, who is reading the results of the race, stops when he sees the raid taking place. However, that was supposed to be a live broadcast from the racetrack itself. It should have continued. Lonnegan isn't stupid - he would pick up on something like that immediately.
Factual error: When Hooker comes out of the diner there is a billboard advertisement to the right. It is for Ezra Brooks bourbon. Ezra Brooks brand wasn't created until 1957.
Plot hole: Doyle attends Gondorff's betting shop three times, and he listens to the announcer calling three races from three different race tracks - Narragansett in Rhode Island, Belmont in New York, and Riverside Park in Missouri. He cannot possibly miss the fact that the same announcer calls all three races! J.J. Singleton, the race caller, has an instantly recognisable voice, and Doyle wouldn't be fooled for a second. Each race track would have had its own announcer.
Suggested correction: There are a lot of things Doyle is processing when he's in the shop. There's a lot happening, and he has a lot on his mind, and increasing pressure and stress each time. It's quite possible that he wouldn't notice the accent of the announcer, something he has no reason to doubt.
Rubbish. During his first two visits, he sits quietly listening to the race announcements. On his second visit, he would recognize J.J. Singleton's distinctive voice and would realize something was very wrong.
Other mistake: Why is the cashier sitting behind bars in the mock-up bookies when he just steps out of the side to go and fetch Gondorf? If anyone wanted to get at the cashiers they could just walk around the side where there is no door.
Suggested correction: It's partly psychological. Also, anyone going around the bars would be slowed down, more than simply reaching over, giving the cashier the opportunity to react.
Other mistake: Wrecking Crew was 3-1. Ray Walston announces he paid $6.00 to win. If he was 3-1, he would have paid $8.00.
Visible crew/equipment: When Robert Redford is being chased by Lt. Snyder, he jumps from a high place to the ground. One can easily tell it's not Redford but a stunt double.
Factual error: The Helvetica typeface, used on the 43rd Street 'L' platform is not correct for the period of the film.
Suggested correction: This isn't a mistake. The person "operating the radio" could easily have switched it off because of the commotion. Lonnegan would simply suppose this is what had happened. He is not going to instantly suspect someone is faking the whole thing.