Finch was nominated for an Oscar for Network and went on to posthumously win the award, which was accepted by his widow, Eletha Finch. Although James Dean, Spencer Tracy and Massimo Troisi were also posthumously nominated for a Best Actor Oscar, Finch was the first actor to have won the award posthumously, as well as the first Australian actor to win a Best Actor award. He was the only posthumous winner of an Oscar in an acting category until fellow Australian Heath Ledger won the Academy Award for Best Supporting Actor in 2009; there were many earlier posthumous Oscar winners in non-acting categories. Finch also won five Best Actor awards from the British Academy of Film and Television Arts (BAFTA), including one for Network.
In 1934–35 he appeared in a number of productions for Doris Fitton at the Savoy Theatre, some with a young Sumner Locke Elliott. He also worked as a sideshow spruiker at the Sydney Royal Easter Show, in vaudeville with Joe Cody and as a foil to American comedian Bert le Blanc. At age 19 Finch toured Australia with George Sorlie's travelling troupe.
In 1954, the Australian journalist and author George Johnston wrote a well-researched series of biographical articles on Finch, his life, and his work, which appeared in the Sydney Sun-Herald on four consecutive Sundays, which were certainly the first detailed account of Finch's life to be published. Finch later provided the inspiration for the character Archie Calverton in Johnston's novel, Clean Straw for Nothing.
Under the Big Top – touring show with George Sorlie, various Queensland towns, 1936, playing Herbert Hughes in Laughter of Fools by H.F. Maltby, Smithers in Married by Proxy by Avery Hopwood, Peter in Fair and Warmer by Avery Hopwood, Hunter in Ten Minute Alibi by William Armstrong – all directed by William McGowan with Murray Matheson, Rosalind Kennerdale, Leslie Crane, Eva Moss, Norman French, Julia Adair and George Douglas.