The film makes reference to famous police detective Dick Tracy, however the film is set in 1928 and the Dick Tracy comic wasn't released until 1931.
Jennifer Grey and Madonna perform a rendition of "I Surrender Dear", however the film is set in 1928 and the first version of the song wasn't released until 1931.
The first line in the opening song, "Big Bucks", is, "The best things in life are free." The audio matches the visual up to "are free", at which point the waiter clearly begins to sing something entirely different.