Audiences at the time would have noticed the "A" gasoline rationing sticker on Granny's scooter. This was the most common level of rationing issued to the general public. It allowed the holder to purchase four gallons of gasoline per week.
The voices of Cinderella and her fairy godmother are imitations of Bette Davis and Barbara Jo Allen (aka Vera Vague), respectively.
Cinderella looks and performs very much like Lou from The Shooting of Dan McGoo (1945), which was released only a few months before this short. Imogene Lynn performed the singing for both characters.
Gone with the Wand is a (corny) pun on the film Gone with the Wind (1939).
The fairy godmother's second mode of transport (created from a trash can) is a US Army jeep, familiar to wartime audiences.