In episodes #2.10 through #2.13 Jeannie wanted to know her birthday. The Show had a contest to guess the month and day. It started with "The Girl Who Never Had a Birthday, Part 1" (#2.10), wherein her year of birth was determined to be 64 BC. As these episodes take place in 1966, Jeannie is 2,029 years old. The actual month and day were finally revealed in "My Master the Great Caruso" (#2.13): Jeannie was born on April 1. April Fools Day, naturally.
Fans of this show - or perhaps Ironside (1967) - will recognize an uncredited appearance of Don Mitchell as the Stage Manager. In three prior episodes, he had played an Air Force Sergeant at NASA: Happy Anniversary (1966), My Master, the Magician (1966), and Where'd You Go-Go? (1965).
The title refers to the famous Italian tenor Enrico Caruso who performed throughout Europe and American in the late 19th and early 20th century who helped promote the home sales of records with his extraordinary voice and career that include over 800 appearances at the New York City Metropolitan Opera House.