Please suppose that instead of a divorce, a parent was a widow(er) or a single parent from the start. Would having a series of relationships be cause for the Children's Aid and the Courts to apprehend the children and place them in foster care?
You are trying to show that he is an unfit parent, please realize that you have to show this by producing behaviour that would apply to anyone and everyone, not just your ex, your children, but all families.
Also realize that you are focusing on behaviour that is visible, obviously you can use the wonders of the internet to find him on a dating site, and you can keep track of his relationships by asking the children. How would you feel if he was keeping your parenting under a microscope, checking your fridge for expired yogurt or using a web cam to track every time you yelled at the children?
None of us are perfect humans, and none of us are perfect parents. Children are resiliant and can weather some storms and turn out to be decent adults. You may be causing them more harm by setting up an adversarial confrontation than he would by having yet another girlfriend.
You do the best thing for children by taking the high road, and showing them a good example and being a decent role model. Don't focus on criticizing others, you are only teaching them to criticize others including yourself.