I primarily shoot in public because I shoot events and etc. I more than understand the problems you are referring to. Here's some suggestions:
1. The police are your friends, so tell them upfront why you are there shooting and most times they'll even help you out.
2. Photo ID is a huge help and wear it around your neck for all to see. It doesn't have to be a media pass, just a badge with your picture and info printed on it.
3. Always act professional, polite, responsible and respectful of others.
4. Never shoot children in a picture without asking permission from their parents first.
5. Shooting pretty women, they love having their picture taken but wave at them first like you're wanting a smile and trust me they'll pose for you. They may not look directly at you but they'll pose in their own way, here's an example:
6. The only thing else I would add is if you're photographing in public where emotions are running at a high level. Such as a crime scene, wreck, disaster and etc. Expect problems towards you to surface, this is why I don't shoot those types of pictures anymore. These types of shoots are emotionally draining and depressing. Taking pictures of this stuff is a lot different than seeing a picture of it on TV.
Anyways, just some food for thought!