Factual error: When Sally and Bryan are in the street, we can see, at their back, election posters. These posters appeared in 1932, one year after the movie is supposed to take place.
Continuity mistake: During the song "Money, Money", Sally (who is singing with the Master of Ceremonies) has nail polish on. This changes color throughout the song, and in the close-ups this becomes more obvious. At the beginning of the song we see that it is green. Later, while we hear, "You can take it on the chin" we see that it has changed color to red. In the end of the song, while "It makes the world go round" it has returned to green.
Other mistake: The film is set in 1931. One of the characters uses the phrase "plenty of nutting." This phrase comes from the song composed three years later in 1934 for the musical Porgy and Bess.