- Best friends since childhood with Carrie Fisher. He reminisced with her on the documentary Bright Lights about taking her virginity (which she considered a burden) as an act of friendship in London in the early 1970s.
- Son of producer/writer Dominick Dunne and Ellen Beatriz Griffin Dunne.
- At age 18, Dunne skipped college and moved to New York to become an actor.
- Griffin's father was of Irish descent. His maternal grandmother, Beatriz Charlotte Sandoval, was born in Nogales, Mexico, to a Mexican father, Alfredo Sandoval, and a mother from Wyoming, Clara Mathilda Holler, who was of German and Swedish descent. Griffin's mother's other ancestry was Irish and English.
- Has a daughter, Hannah Dunne, born in January 1990, together with Carey Lowell.
- Good friends with Michael Keaton.
- Older brother of Dominique Dunne and Alexander Dunne.
- Founded with Amy Robinson production company "Double Play Productions".
- He and Linda Hamilton were the first "Guest Callers" on Episode One ("The Good Son") of the popular television series "Frasier," which aired on September 16, 1993.
- Studied acting under Uta Hagen.
- He studied drama at HB Studio in Greenwich Village in New York City.
- Nephew of John Gregory Dunne and Joan Didion.
- Frequently works with actress Rosanna Arquette.
- Cousin of Quintana Roo Dunne.
- Cousin-in-law of Gerry Michael.
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