I'm not too familiar with widespread USA words that aren't used elsewhere. I don't really pay attention but I'm also not sure if we have anything.
On the topic of police officers though, we could probably fill a page with the words we use for them. The ones only off the top of my head are police, cops, fuzz, heat, coppers, black & whites (not used so much anymore, since most police cars aren't black/white anymore), pigs, 5-0 (pronounced five-oh), and Feds (usually meaning FBI). It probably differs by region, but more people say "cops" than "police/police officer".