Dun has had prominent roles in several films, notably Year of the Dragon (1985), Big Trouble in Little China (1986), The Last Emperor (1987), Prince of Darkness (1987), and A Thousand Pieces of Gold (1991), Warriors of Virtue (1997), . In addition he has appeared in independent Asian American projects such as My American Vacation (1999) and My Life Disoriented (2006). For four seasons he was a regular cast member on the NBC television series Midnight Caller (1988–1991).

Dun began acting at the Asian American Theater Company in San Francisco. He has appeared onstage at East West Players, Berkeley Repertory Theatre, and Lodestone Theatre Ensemble. For his performance in Chay Yew's A Language of Their Own at the Celebration Theatre, he won an LA Weekly Theater Award for Ensemble Performance (shared with Noel Alumit, Anthony David and Chris Tashima). He has participated in both the film and theatre labs at the Sundance Institute. Dun wrote and performed the one-man show Giant Oranges, commissioned by the Mark Taper Forum and produced by Yew's Solo Works Festival in Los Angeles.