I understand that a policeman in Israel can stop a car and go over any prohibition stopping him, but does this allowance to stop extend to people driving their cars on shabbat? Is it still breaking shabbat to stop the car or is it mitigated by the fact that its necessary for security?

Obviously people should not be driving on Shabbat, and we should try and minimize their transgressions as much as possible. On the other hand, if there is a security need to stop cars, which supersedes Shabbat, we can't differentiate and those sinners need to comply as well. As always, the policemen should try and minimize the Shabbat desecration as much as possible.