Crossword puzzle clue "cops in slang or a hint to this puzzle's theme"

Cops, in slang ... or a hint to this puzzle's theme

Hint (and a hint to this puzzle's theme)

Puzzle invented by Lewis Carroll (and a hint to this puzzle's theme)

Carol sung by the cops from "Cops"?

Cops, to people who dislike cops

Contented sighs (and a homophonic hint to this puzzle's theme)

"Dog the Bounty Hunter" network, and a hint to the theme in this puzzle's four longest answers

2014 NBC comedy starring David Walton ... and a hint to the puzzle theme which is ___