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.
Factual error: When Lonnegan brings the briefcase full of money to the cage for his big bet, all of the 100s in the case are 60s federal reserve notes, which obviously did not exist in the 1920s or 30s.
Factual error: The Helvetica typeface, used on the 43rd Street 'L' platform is not correct for the period of the film.
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.
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.