What I was suggesting is really just inspired by most books and shows I have seen/read recently. Both media often reveal their (often not yet created until you read it) backstory, with details and so on. Often this includes learning things about characters where they colluded with cover ups, committed crimes, or otherwise know more than most about what happened and how it was resolved in a dirty/messy fashion. Cuz how would you know what there really is to know, if you weren't behind closed doors etc? It can be violations of codes or laws, atrocities or actions out of keeping with the desired image, it could just be the sausage factory that is politics, as long as you have something to lose if it's brought to light.
HOW you do it is a matter of taste and complexity. Linking it to the Secrets rating makes it mandatory and tracked by the same Merit.
You could (less) easily throw in Dirty Secrets as another flaw type thing, and let people define it however they like, including linked to the City Secrets.
I like noir, and the intimacy of a shared difficulty, even between rivals or frenemies.