When Rogers explains to Cindy what his wife is trying to do she says that it's just like a movie with Greer Garson, Ronald Colman, and Vivien Leigh. Those three never worked together in a movie, but Garson and Colman were in Random Harvest (1942) together, although the plot of that movie didn't match the one she described.
When Lilian Gish is telling Isaac how there's no shame in being a bartender, she says 'It's not who you are that matters, it's what you are that counts'. It should be the other way around.