Pennies from Heaven (1981)
Peter's character sings two lines from Singin' in the Rain.
When Eileen and Arthur are in her kitchen discussing her pregnancy, she begins grinding coffee beans in a hand grinder (iron box with grind handle in lid), just as Maria, the pregnant maid in Umberto D., does during a kitchen scene in that film.
Title mentioned by Peter Lamont
Filmographical reference re Ken Adam
Musical numbers happening in characters' minds
porn title seen: "Penis from Heaven"
Clip of Christopher Walken shown in a segment on the music video of Weapon Of Choice, in which he starred.