There are a few items at the vatican. I only remember slivers of wood from the cross he carried and a cloth that someone wiped the sweat from his face and his image remained imprinted. I wish I could remember more...but is it really that important?
I prefer to believe that he does exist, otherwise what are we doing here? And I would prefer to believe that we do go to a better place when we die.
As far as the movie, I think it's just another attempt to destroy the faith of those who do believe.