I'm not sure what you are looking for here.
What about an airline crash, for which the NTSB does not find a solution? Or reported sightings of UFO for which there is not enough evidence to be sure if it is a hoax or just venus? Or just an unsolved crime?
There are lots of mundane unexplained things.
If you are looking for hard problems, I suppose consciousness is one of those - see
You are.
Are you looking for a
Coffee House discussion, where people just add their own items? Or are you looking for one or two big ones, with perhaps a discussion of why it is a difficult problem. Maybe we would put that in
Creation/Evolution Miscellany.