That is a fun one!
I feel like such a dud because I can't think of any weird reference questions. It has been a long time since I was actually working on a reference desk; I love reference, though, and miss it terribly!
My favorite, or shall I say most memorable, reference question was about who actually said "The business of America is business." Coolidge is often attributed the quote, but it was actually William Allen! I remember this because I had just published a Masters thesis with the mis-attributed quotation at the head of one of my chapters!!!