Disney's original film and its sequels include examples of:
Dueling Movies: In 1950, a Spanish animation company called Estela Films also released an animated version of the Cinderella story, called Erase una vez.... Disney obviously won, with the former being a lost film.
Supposedly, Disney was aware of the Spanish film and copyrighted the name Cinderella/Cenicienta in Spain, so they could not use it for their film's name.
What Could Have Been: Prince Charming originally had more screentime. In a deleted scene, he was seen apparently hunting a deer, but it turned out they were friends and playing a game together, and in another, he's reintroduced to Cinderella after she fits the slipper. While surprised that she was a servant, he accepted her immediately.
At one point Cinderella and her Prince were going to be shown having a dance among the clouds, based on an abandoned concept from Snow White, but it didn't make the final cut. This twice abandoned concept was later used at the end of 1959's Sleeping Beauty.
Originally Cinderella had a song where she lamented her situation called The Cinderella Work Song, which came complete with Cinderella fantasizing about multiplying herself into an army of maids to take on her ever growing work load.
A scrapped scene had Cinderella returning home from the Ball and overhearing her evil stepmother and stepsisters talk about the mystery girl from the Ball who had charmed the Prince - and Cinderella is shown to be deeply amused by this since she knows they're talking about her. Apparently old Walt Disney himself had the scene cut since he thought it made Cinderella look vindictive and thus unsympathetic.
Viewers Are Geniuses: "I'll name you Octavius, but for short we'll call you Gus." Octavius was the nephew Julius Caesar and his heir by adoption. Upon becoming emperor he was renamed Augustus Caesar. "Gus" is shorter form of Augustus/Augustine.
The 1957 production of Rodgers and Hammerstein's version contains examples of:
Blooper: During a reprise of "Do I Love You Because You're Beautiful?", the camera closes up on Queen Constantina preparing to sing a line, but Prince Christopher interrupts. Jon Cypher apologized to Dorothy Stickney later that night.
Hey, It's That Girl!: Julie Andrews played Cinderella eight years before starring in the film version of Rodgers' and Hammerstein's The Sound of Music. King Maximilian's actor, Howard Lindsay, also happened to become co-writer of the original Broadway version of Sound of Music.
Missing Episode: People living on the East Coast saw the musical live in color, while those in the west saw a black-and-white kinescope. The DVD only contains the latter version.
The 1965 remake of Rodgers and Hammerstein's version contains examples of:
Dubbing singers Bill Lee note the singing voice of Captain Von Trapp in The Sound of Music and Betty Noyes note the uncredited singer of "Baby Mine" from Dumbo play townspeople during the "Prince Is Giving a Ball" number.