To get your Righteousness back up to four and even to five stars you have to go and graffiti the people you visit and clean up their towns of graffiti. Also, if you see graffiti in your town cleaning it by clicking on your school, town hall, police station, and Moe's will affect that. I was able to raise my righteousness back to five stars by simply graffiting and cleaning up in other people's towns and my own. I think having a decent number of friends, say around fifty, helps because you can do nothing but a graffiti run and it will help boost your stats there.
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On the other hand, sending Mayor Quimby on a 24 hr task to embezzle money dropped me from 5 stars to 2 stars.
The best thing is to graffiti or to clean graffiti off in your friend's Springfields (only 9-10 buildings needed, so only 3-4 friends with enough buildings?), plus keeping Chief Wiggum and Mayor Quimby from taking bribes, etc. (plus maybe keeping Snake in jail, and Fat Tony and Muntz out of trouble?).
It's really random. But.....I have noticed it happens alot more often.