Anthony Quinn had a broken foot during filming, and thus couldn't perform the dance on the beach as scripted, which called for much leaping around. Instead, he did a slow shuffle. Director Mihalis Kakogiannis asked Anthony Quinn what the dance was, and Anthony Quinn made up a name and claimed it was traditional.
Simone Signoret was the original choice for Madame Hortense. After filming began, director Mihalis Kakogiannis realized that she wasn't what he wanted for the part and asked permission from Darryl F. Zanuck to replace her. He agreed and he proposed Bette Davis. Kakogiannis, though, had Lila Kedrova in mind. Zanuck had no idea who Kedrova was, or how she even looked, but he trusted Kakogiannis very much, so he agreed.
The original Broadway production of "Zorba" opened at the Imperial Theater in New York on November 16, 1968, ran for 305 performances and was nominated for the 1969 Tony Award for the Best Musical. Anthony Quinn and Lila Kedrova who starred together in this movie version appeared in the revival of Zorba in 1982-3 with Lila Kedrova winning the 1984 Tony Award for Best Featured Actress in a Musical. "Zorba" was nominated for the 1969 Tony Award (New York City) for the Best Musical.
In the earlier stages of filming, Mihalis Kakogiannis and Anthony Quinn had frequent disagreements as the director felt that his leading actor was being too over-the-top.
Simone Signoret was offered the part of Madame Hortense initially, and turned it down. She regretted that decision, (she explained to me) they gave it to Lila Kedrova who ended up receiving an Academy Award for her role.