I suspect that the MPD (and everyone else, for that matter) treats Superman as a de facto member of law enforcement - that's what made Mayson's attitude so different - she considered him a vigilante, not a member of a law enforcement team.
As for Luthor, Superman has abducted him and is guilty of unlawful imprisonment as well as taking him across international boundaries.
Then again, if Superman is right and Luthor's empire collapses, Luthor will be too busy running to try to expose what Clark did to him.
