Well, I'm not convinced he was born in 1912. When the Academy of Motion Picture Arts and Sciences (who mantain a database of information on all members past and present) were consulted on this matter in 2007, they responded thus:
"We did some research into Peter Finch's birth date and do not find convincing evidence to warrant a change to 1912. His birth date has been consistently reported as September 28, 1916. Recently the IMDb has changed the birth year to 1912, apparently to match the dates on Finch's grave marker, but no written documentation has been found to support this date. The year is given as 1916 in the California Death Records and in a memorial advertisment in The Hollywood Reporter placed by his widow after his death. Biographies by Trader Faulkner and Elaine Dundy, both published after his death, refer to the circumstances of his birth taking place during World War I. Both authors interviewed Finch's mother, who survived him. Dundy's "Finch, Bloody Finch" (1980) cites marriage and birth records as well as family correspondence, which all support the 1916 date."

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His ex-wife said that he died at the age of 64, meaning that he was born in 1912. http://www.vivandlarry.com/vivarticle5.html. Still he never looked very old, considering his lifestyle. I have trouble believing he was 64 when he died, but the man did have some luck on his side
Also: http://s3.amazonaws.com/findagrave/photos/2002/139/337_1021936157.jpg

I think 1916 is more accurate than 1912.He was reported to be younger than Vivien Leigh at the time of their affair, and Vivien was born in 1913.

IMDB is going for 1912 as it's the date on his gravestone. But gravestones can be wrong. As far as Im know there's no ohter evidence to show he was born in 1912.