It sounds ideal in principle - as so many notions do - that we know the criminal pasts of our neighbours.
But the difficulty lies in the fact that there are those whose misplaced sense of self-righteousness leads directly into actions of a vigilante nature, and that is a very slippery slope indeed.
On the basis that a paediatrician was assaulted by individuals in his neighbourhood whose self-righteous application of mob rule prevented them from ascertaining what his job title actually meant, I would be against everyone knowing everyone's legal history.
The law applies punishments, and once completed, they should not follow an individual around for the rest of their life - that is not now a civilised society works.