Yes, "Schrodinger's Cat" even though this paradox has been greatly exagerated as you said yourself :
"I would have been happier if they had stuck to real science... that's weird enouh without having to invoke spirits! "

Actually a cat remains a cat , it is not everywhere, the collapse of the wave form being implicit in the "cat" itself same as in any other "real" object

Even some real objects have a sort of "double face "
There are some materials which normaly are in a fluid and non magnetic state
but if you touch them they turn in a solid and magnetic state
The magnetism must be already "hidden" somewhere

The real mistery is the " non locality " rather than the double state wave \ particle
If you splits the wave into two parts they keep behaving same as they were one only wave