- Had a hit record "Valley Girl" with her father in 1982. The single helped launch the brief Valley Girl fad of the '80s.
- Got her middle name from the idea that her birth made parents Frank Zappa and Gail Zappa a "family unit".
- Her name is parodied in Austin Powers: The Spy Who Shagged Me (1999). Dr. Evil's moon base is divided into two units, "Moon Unit Alpha" and "Moon Unit Zappa".
- Daughter of Frank Zappa and Gail Zappa.
- Her ex-husband, Paul Doucette, is the drummer with the rock band Matchbox Twenty.
- In 2004, Moon Unit was voted the most bizarrely named celebrity offspring off all time in a poll for Sky TV.
- Gave birth to her 1st child at age 37, a daughter Mathilda Plum Doucette on December 21, 2004. Child's father is her now ex-husband, Paul Doucette.
- In November 2005 she topped a list of celebrity offspring with the most bizarre names, according to an on-line poll.
- Her vocals on "Valley Girl" were unplanned. Frank Zappa was working on the track and needed a female voice to do the lines, so he went upstairs and asked her if she wanted to do it. Moon had been missing her dad, who'd been busy recording, and asked to "book a session" just for the chance to spend time with him.
- Ex-sister-in-law of Selma Blair.
- Sister-in-law of Shana Muldoon and Patrick Muldoon.
- The following television shows and films were aired/released on her birthday:
- The Code (1969)
- Gossip (1974)
- The Price of Liberty (1975)
- Time After Time (1979)
- The Leap Home: Part 1 - November 25, 1969 (1990)
- The Principal and the Pauper (1997)
- Toy Story (1997)
- Trust Metric (2007)
- Sex, Pies and Idiot Scrapes (2008)
- Dead Wrongs (2010)
- How Much Pain Will It Take to Crush Inflation? (with Minneapolis Fed President Neel Kashkari) (2022)
- She also has the same birthday as Confucius, and Cathriona White died on her birthday
- Moon Unit Zappa died 3 years to the day before she was born.
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