I didn't go through all the posts, so I don't know if anyone mentioned this. In most areas, police cars and police officers are exempt from all traffic laws. However, if there are injuries or deaths due to the officer's actions, it will be investigated as to whether or not he/she was doing something he shouldn't have been.
But, you are right, traffic is supposed to stop for people in a marked crosswalk and they always have right of way at all intersections. If they cross in the middle of a block, it is jaywalking and they can get a ticket, but that doesn't mean that someone can run them over.