This involves everything from the rampant crime the player is able to get away with to beating people up and them just not caring and anything else that could have something reasonable.
For Crime : The obvious change is your fines(if spotted) should not go away once leaving a building. An addition that would be fantastic naturally is the AI trying to call the enforcers if they spot you or if you get away with spotted crimes and they report you.
I'd love to see a system where the fines the player gains would gather attention from the enforcers, with them being able to spot you in the streets to maybe even trying to man-hunt you and staking out your apartment if you're being an especially big trouble maker. Being arrested by an enforcer would entail a time skip similar to normal pass-out that scales based off the fines you have with a maximum to how long you'd be stuck, maybe even a bail option.
This goes with another suggestion concerning assaulting people or being caught in general : NPCs will change their disposition to you depending on what you've done to them and for them. Obviously being caught sneaking in someone's home is bad, maybe you could get away with a sorry as long as you can prove it was you just doing an investigation but if you end up in combat or chasing them and knocking them out? I doubt they'd ever have a good opinion of you after that, meaning it'd be harder to get information out of them if at all.
Consequences don't have to be entirely negative either, despite how ominous the word sounds or it's typical use. We could get positives like giving money to the homeless will naturally increase disposition with them and may get us some street info from them, maybe in the future if rent is ever a thing we could get good with the land lord of our place and work out better deals with them, maybe even get access to someone's apartment through a favor.
I'm sure many others have similar and other ideas of how this could all be handled as well.