Starting out in vaudeville as a comedian, Moore enjoyed a fair measure of success for more than two decades before making his breakthrough. He made a few appearances on Broadway, including Rosemary (1896) and two later shows for George M. Cohan, Forty-Five Minutes From Broadway (1906) and The Talk Of New York (1907). He continued in vaudeville, with occasional parts in big productions, always in comic roles, and from 1915 appeared in numerous silent films, including Snobs (1915), The Race and The Clown (all 1916) and The Man Who Found Himself (1925). By the mid-20s he had become very popular on the stage and played Shorty McGee in Oh, Kay! (1926), and five years later co-starred with William Gaxton in George Gershwin and Ira Gershwin’s Of Thee I Sing (1931). It was this informal partnership that brought Moore most recognition. Gaxton and Moore honed their routine, of debonair leading man and bumbling buffoon, through several more Broadway successes. These included Cole Porter’s Anything Goes (1934), Irving Berlin’s Louisiana Purchase (1940) and Nelly Bly (1946). Moore also appeared in Porter’s Leave It To Me! (1938).

Meanwhile, Moore had continued with his film career, appearing in Dangerous Nan McGrew (1930), Romance In The Rain (1934), Swing Time (1936), Louisiana Purchase (1941), Star Spangled Rhythm (1942), Riding High (1943), Duffy’s Tavern (1945) and Ziegfeld Follies (1946). In his later years, Moore appeared in some non-musical films, including the star-studded We’re Not Married! (1952) and The Seven Year Itch (1955). In 1957, Moore made his final stage appearance in a revival at New York City Center of Richard Rodgers and Oscar Hammerstein II’s Carousel.