search and seizure

police impound car,do an invintory
on the contents,while doing
invintory they pick up the mat in
the hatch back,finding contraband.
then apply for a search warrent
after the fact

Yes, if the impounding was legal, then, in at least most states, an inventory search is routine and legal. If an illegal substance is found during a legal search, the contents are admissable, and they absolutely did the appropriate thing by obtaining a search warrant before continuing the search.