Mr. Walt Disney is the mystery guest on What's My Line? from the November 11, 1956 episode according to the original poster. Which means that the Mickey Mouse Club was a year old and Lady and the Tramp had come out the year before. Disneyland had just opened its doors in 1955 as well.

There's also a Jerry Lewis pre-telethon call for donations against muscular dystrophy.

Direct link for the feedreaders. Sent over by Ken.