One of his first roles was that of Nick Dutton, the son of an industrialist who knew the truth about his family's new butler and housekeeper, and helped them get acquainted in their new jobs in the 1971 situation comedy The Good Life.

Among his other early roles on television were appearances in the TV shows That Girl; Room 222; The Partridge Family; Love, American Style; Needles and Pins; Columbo; Baretta and Chico and the Man.

Goldman was also featured as Ozzie the Answer in the 1980s detective drama Mickey Spillane's Mike Hammer and as Dr. Denton on Get Smart, Again!

TV program during its syndicated run, and on the live stage version in Hollywood several years later.

Other credits included a small role as a persistent medical student who asks Dr. Frankenstein (Gene Wilder) about his grandfather in Young Frankenstein (1974), and roles in Busting (1974), Linda Lovelace for President (1975), Tunnel Vision (1976), The Missouri Breaks (1976), Swap Meet (1979), Wholly Moses!