I'm sure all the people that let Bernie Madoff "invest" their money felt that they had a good idea of how trustworthy he was from all his references as well...
Lots of identity theft happens with family members using a person's ID.
I'm sure I think that I know which of my friends and acquaintances are honest and which are not. I don't really know if I am right or wrong.
As far as checking up on someone goes, it may actually be easier to do it if you are meeting someone on OKCupid or the like, because you can ask them upfront about it, and offer the same to them. Just like STD testing. There is less likelihood that they will be deathly offended if you ask them for permission to check, than someone that you had met more organically through friends or clubs.