Just a sidenote on all the "one stray shot" comments: that's simply not true. As long as the damage you do to a targets shields is below a certain threshold, all it does is complain, without you being considered a criminal. So yes, if you land your double C4 PA salvo on an unsuspecting target, you of course go criminal right away, but just a stray shot of your MC or laser won't be a big deal.
And in the end, it's really just about trigger discipline. I would not be aware of any legislation or military, where "he ran into my line of fire" would be an accepted reason for shooting somebody.
That being said, i also think that C&P in the current state is not that great. But my point of view is just the opposite of the OP: once you understand the system it's inconsequential. It doesn't do its job, as it can be avoided way too easily. Just pay a tiny bit of attention on where you are going or switch your ship, notoriety will then go away by itself again.
I would prefer if it would have more meaning, e.g. notoriety would stay on you till you actively get rid of it. Which would require to do redemption missions or something like that. It should have more significant consequences than it does now. But high notoriety should also grant access to specific content. (Possible content for that would be crime lords which only interact with you when you have a certain notoriety level. While in turn there could be other places where your options will permanently be limited if you ever in your commanders lifetime went over a certain level of notoriety. You built up notoriety, even if you are cleared by the law, your history remains and some people don't want to be seen with you. )
But that all, while being new content and being interesting, also would be work to implement. I am not holding my breath...