Jeter made his film debut in the anti-war musical Hair 1979 as Woodrow Sheldon. He appeared in films including Ragtime 1981, The Money Pit 1986, and Tango & Cash 1989. His television role as the nerdy math teacher Herman Stiles on the sitcom Evening Shade 1990-1994 earned him a Primetime Emmy Award for Outstanding Supporting Actor in a Comedy Series.
On stage, Jeter won a Tony Award for Best Actor in a Musical for his role in Grand Hotel in 1990. He continued to take supporting film roles, such as a homeless cabaret singer in The Fisher King 1991, Father Ignatius in Sister Act 2: Back in the Habit 1993, the inventor Old Gregor in Waterworld 1995, the alcoholic clown Norm Snively in Air Bud 1997, and the condemned prisoner Eduard Delacroix in The Green Mile 1999.
Jeter earned two additional Primetime Emmy nominations for guest roles: for Picket Fences in 1993 and Chicago Hope in 1996. In 2000, he began playing the silent mime character Mister Noodle, the brother of Mr. Noodle, on Sesame Street’s Elmo’s World segments, a role he performed until his death.