What a delight to find this thread! I've just been watching a DVD of Emir Kusturica's "Otac na sluzbenom putu" ("When Father Was Away on Business" in US release). The haunting melody woven through the film took me a moment to recognize as "Anniversary Song" from Jolson's movie, and I got curious about the melody's origins.

Thanks to all who've contributed to this wonderful journey of discovery. Oh, how I love the web!