Prince Edward's line, "I have loved but once. I have loved but you, and I have lost you twice" is a reference to Roxanne's line, "I never loved but one man in my life, and I have lost him twice."
The scene ("Tell Him Anything" number) where Chamberlain, instructed by Prince Edward's father, tells Cinderella to leave Prince Edward is a reference to "Camille" (or "Lady of the Camellias"), in which Armand's father tells Marguerite to end her relationship with Armand, and she leaves Armand under the guise of no longer loving him.
Poster, stills shown.
Frost is one of the producers of the film, and is seen at the movie's premiere
The "Be Our Guest" number is reminiscent of the kitchen dance in the number "Position and Positioning."