A 30 year old chap in your street is having sex with 16 year old school girls in the area.
How would I know for certain this guy on my street is having sex with 16 year old school girls?
He’s also a creepy sex pest in public.
Have the police been alerted to his creepy sex pesting?
He gets barred from the local shop and pub
Why? If this because of a rumour going around?
a few of the girls fathers have filled him
There's allusion here of him being assaulted. This is a crime, if he didn't fear for his life, he would report it to the police. He doesn't.
He’s generally not liked and accused of forcing himself on girls.
So no proof, just a bit of a weirdo and there's a few stories going around.
Your brother hears about this man and owns the local petrol station in the next town. Your brother is outraged and bans this man from using the petrol station where his daughter works.
The man turns up to the petrol station, my brother is angry after hearing all the stories and wants to put an end to it to protect his daughter. He fills him, then douses him in petrol and sets him alight. One less perve in the world.
He gets life for murder. An investigation finds that none of the things that my brother thought this guy had done, were proven to be true.
Everyone.
Yes, I've butchered your post and sensationalised it, but I do however agree with the sentiment of your proposal - people in an area will act to protect and look out for each other, especially with how awful the police are in some places, so a degree of self policing occurs. However, the mob can and does get carried away and has to be guarded against somehow.
I knew a few loner guys that have had rumours passed around, one guys was terrified to be seen out in public because of what people were saying about him. It wasn't true, and never found out how it started, mistaken identity maybe - the guy had to move in the end. I'm personally ashamed, that as a kid, I spread a horrid rumour about my neighbour - I never got a chance to apologise.