Your approach to make people post something on Twitter
is the most inappropriate solution to your problem.
The reasons:
1) Risk of not solving the problem. It's not a bold thing that you do. Instead, be a direct person and speak with someone
2) Can you prove the guy's past? If yes, how? If it's already in the news, why not sending it to your employer?
3) The guy's life is already thoroughly damaged, his reputation is not the best. Why do you want to make it worse? Just because he treats you bad? Why not telling him in private that, if he doesn't continue to behave ethically you're going to expose him?

In United Kingdom we have something called "whistleblowing" which is more related to businesses rather than individuals, but it can apply to your case. Basically, you bypass information of wrongdoing and you are protected by law, nobody can take action against you. The most important thing is to act in the benefit of the public.