In a stage production Barbra while dancing on a prop cigarette holder drops a cane, runs along the holder to the side of the stage where she has the cane in her hand.
Near the end of the movie, in a meeting between Brice and Rose, they discuss his divorce from Eleanor Holm. Rose and Holm divorced three years after Brice's death, so the discussion could not have taken place as portrayed in the film.
Near the end of the movie, in a meeting between Brice and Rose, she quips they were married for four years. In reality, they were married for nine years.
Near the end of the movie, in a meeting between Brice and Rose, he mentions taking over the Ziegfeld Theatre. Rose took over the Ziegfeld Theatre after NBC dropped their lease long after Brice was dead. The discussion could not have taken place as portrayed in the film.
In the rainy scene where they are leaving the theatre, there are signs posted about "Crazy Quilt" in its 5th month. The show only had 79 performances from mid-May to July, 1931.
When Fanny makes an unexpected visit to Billy's "Aquacade" (Great Lakes Exposition, 1937) they are walking by the pool, and having a private conversation before the dress rehearsal. A jet aircraft can be heard flying overhead. The very first aircraft to be jet powered was flown on a test flight in Germany, August 1939.
Fanny's black tennis shoes - worn for comic effect in the 1937 Aquacade number - aren't period-correct: it wasn't until 1949 that Converse decided to make the toe guard, laces and outer wraps on black "Chuck Taylors" a contrasting white.
When Fanny Brice takes off, singing, in the yellow biplane, the plane is shown taking off from a runway clearly marked with Instrument Landing System (ILS) bars, which had not yet been developed in the late 1920's when the scene is set.
In the "How Lucky Can You Get?" musical number, when Fanny is turning on the stage lights she is clearly not singing, although Streisand's singing voice is heard on the soundtrack.