Over the radio, a police dispatcher tells the two radio policemen that Wally Storm, a.k.a. "Bulldog Banks," is to be apprehended because he escaped from prison on June 6, 1933. Yet, earlier in the film, he wasn't indicted for his "crime" until August 9, 1933, as indicated by the shot of the front page of the newspaper that had an article about his case. In other words, he couldn't have escaped from prison several months *before* his trial had even started.
During the in-car shots of the big race, there are several breaks in the rear screen projection footage behind Wally and Pat - either jumping to different parts of the race track, or to a different race track altogether.
Storm has the plane land on the infield of the "Dayton 500" race, and there are mountains visible in the background. There are no such mountains near Dayton, Ohio - or Indianapolis, Indiana for that matter.
When Johnny has the fight in the pits after the race at the beginning of the film, a clear shadow of the boom microphone is visible on the ground behind him.