The Object of My Affection (1998)
When George and Nina take the ballroom dance class, at one point, they are waltzing to a song from this film and Nina is wearing a long blue scarf similar to the scarf-y dress worn by Debbie Reynolds in the dance to the same song in "Singing in the Rain."
Video case is shown in a video store.
An interviwee in the film mentions this film.
In the short "The Woods," Paul Rudd guest stars. There is a moment where each character gets their own retrospective flashback scenes, and they flash back to scenes from this movie