Dudley Moore was originally cast in the role that went to George Segal. He was fired by Barbra Streisand for not remembering his lines. These were the first symptoms of Progressive Supranuclear Palsy, a brain disorder that would later kill Moore. Conversely, in the earlier 10 (1979), Segal was replaced by Moore.
Barbra Streisand revealed in an interview given in 2014 that Lauren Bacall had some troubles with the scenes in which her character was more vulnerable. So Streisand stop the filming to help her through those moments, but she secretly told the cameras to keep rolling on Bacall. That's how the director was able to get the take that is finally on the movie, because thinking they were just rehearsing and without the pressure, Bacall was able to connect deeply with her emotions.
When Rose (Barbra Streisand) is putting things in Greg's (Jeff Bridges') house she puts up a picture of her parents. This picture is of Barbra Streisand's real father, and a picture of Lauren Bacall replaced Barbra's real mother.
On-location filming at Columbia University caused a campus-wide blackout one day.