I was thinking it may be hard on the engine to try and add a whole new status to people based on the character, but I would think that getting to know your fellow citizens and having them like or dislike you due to actions/gifting/helping solve cased would be cool.
People that like you may be more willing to give more detailed advice or information on people they know, and people that dislike you due to beating up them, their coworkers or relations would be kinda cool.
Not sure if it's feasible, but I think it would be an interesting mechanic and bring the city and it's people into the fold of your life more readily.
Didn't see a thread for this specifically yet, but if there is let me know.