His father was a member of the Austrian Nazi Party who volunteered for the infamous SA and became a ranking officer. In the early '90s, Spy Magazine printed his father's Nazi Party membership in their magazine.
After several public claims of racism were made against him that could effect his career and long-term political chances, Schwarzenegger donated substantial sums to the Simon Weisenthal Center in Los Angeles and commissioned an "audit" of his father's nazi past, essentially buying off potential criticism. He never distanced himself from Kurt Waldheim, however -- quite the opposite. He made a statement to friends , saying "My friends don't want me to mention Kurt's name, because of all the recent Nazi stuff and the U.N. controversy, but I love him and Maria does too, and so thank you, Kurt."
March 1992 Spy Magazine article mentions a story confirmed by "a businessman and longtime friend of Schwarzenegger's" -- that in the '70s Arnold "enjoyed playing and giving away records of Hitler's speeches."