- Was offered his role in The Nightmare Before Christmas (1993) while swimming in the backyard pool of Tim Burton. The two had been friends since working together in Beetlejuice (1988).
- Lost his Victorian-era home in Bessemer, Alabama, together with all of his belongings, in a 2008 house fire.
- Underwent gastric-bypass surgery in April 2002 with the help and support of Michelle Phillips and Carnie Wilson. He lost over one hundred pounds.
- Glenn became close to Tennessee Williams in 1977, during his work as a Production Assistant on "Vieux Carré" at the St. James Theater in Manhattan. The star was Sylvia Sidney, who Glenn later costarred with in Beetlejuice (1988) and renewed his friendship. Spent long hours at the Monkey Bar at the Èlysèe Hotel with Tennessee where he prepared Glenn for the pitfalls of fame and notoriety as well as his philosophy of artistry.
- Frequently cast in Tim Burton's films.
- He played Roman emperors Caligula in Salem, the Boy (1999) and his uncle Claudius in Trailer for a Remake of Gore Vidal's Caligula (2005). His character in Beetlejuice, Otho, had the name of another Roman Emperor.
- In 2005, took a four-year sabbatical, which officially ended when he co-starred in the feature film, Finding Gauguin (2010), which wrapped on Maui in August, 2009. (September 2009)
- In 1974 attended Birmingham Southern College on a drama scholarship.
- Lived in Toluca Lake, California, while still taking on various roles in film, television and cable-network productions. Also touring the United States and abroad for fan conventions. (February 2004)
- Became a member of The Ensemble Studio Theater in 1986.
- Former neighbor of Xander Berkeley in the 1980s when the two lived in neighboring apartments in Hollywood.
- Lived in a beautiful Victorian house in his home town of Bessemer, Alabama. (May 2008)
- Upon his death, he was cremated.
- He was a lifelong Democrat.
- Second cousin of John Rothman and Tom Rothman.
- Born on exactly the same date as Sam McMurray of "Likely Suspects" fame.
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