In 1914 he fought Jack Johnson for the Heavyweight Championship of the World, and in 1916 "The Fighting Dentist" went up against Jess Willard for the same title, but lost both bouts.

[11] It was Moran who, as a cop in Sturges' Christmas in July (1940), halted a tirade by an argumentative Jewish storeowner by barking, "Who do ya think you are, Hitler?"

[10][12][13] Also, at the beginning of his acting career, Moran was part of the featured cast in Raoul Walsh's Sailor's Luck (1933).

[14] Other notable films in which Moran appeared include Charlie Chaplin's Modern Times 1936, Fred Astaire and Ginger Rogers's Follow the Fleet, Shall We Dance, and Carefree (1938), Frank Capra's Meet John Doe (1941), 1943's Lady of Burlesque starring Barbara Stanwyck and Road to Utopia with Bob Hope and Bing Crosby (1946).

Moran's final film appearance was an uncredited bit part in The Iron Sheriff, a Western, in 1957 at the age of 70.