When Jerry (Russell Hopton) shows Bert (James Cagney) his money-making scam of selling "swastika charms", there is an abrupt edit, probably a closeup of what the charm looked like. Swastikas were considered good-luck charms until the advent of the Nazis two years after this movie was released, and the edit almost certainly took place between then and 1941 when other war-related edits took place in Hollywood (e.g., anything relating to Italy in The Marx Brothers' A Night at the Opera (1935)).
It appears a real bottle of Old Grand-Dad bourbon whiskey - 100 proof "Bottled in Bond" - is found in the back seat of Johnson's car when he's out "parking" with Anne. Unusual product placement during Prohibition. Other such bottles can be seen throughout the film. It was allowed to be distilled under strict government control during Prohibition for "medicinal purposes".
Bert is reading a real copy of Success magazine, which was founded in 1897 to promote the "New Thought" philosophy. The issue date at the top of the cover has been taped over or cut off.
James Cagney took this film to avoid being typecast after the success of The Public Enemy (1931). Ironically, he's still playing a criminal, but he's expanding out into comedy and romance here.
One of the racehorses is named is Mile Away. Mileaway was the name of James Cagney's character in his second of two pre-fame co-starring roles in The Doorway to Hell (1930) starring Lew Ayres.