Continuity mistake: When Lt. Snyder breaks the phone booth window with his gun and points it at Hooker, Hooker's hat falls off. Yet in the next shot over Lt. Snyder's shoulder you can see that Hooker's hat is back on his head.
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.
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.