So, the police will sit on their hands for two years on the gang-rape of children. But if you post a satirical picture of them, they'll threaten you with imprisonment. Again, I think that speaks volumes about their priorities. Its all about protecting themselves from scrutiny and criticism, not about protecting us from criminals.
But besides being vile, their threat isn't even legal. The law they cite - section 49 of the Policing Act 2008 - criminalises
without reasonable excuse, carr[ying] on an activity under an operating name that includes the word "“Police”" or the words "“New Zealand Police”", in a manner likely to lead a person to believe that the activity is endorsed or authorised by the Police or any part of the Police.
And this simply doesn't apply. The Daily Blog isn't using either of those terms in its name (they're not "The Daily Police Blog", for example). They're not passing themselves off as being an official police publication, or endorsed by them. As for the picture in question, its is clearly satirical, and again there is no chance of people mistaking it for an actual police advertisement. And to the extent that there is, it is clearly political speech, enjoying the very highest level of protection under section 14 of the BORA.
My (unlawyerly) advice to the Daily Blog is to put the picture back up, and tell the police to fuck off, and sue them into the ground if they do anything.
(I should note: the picture in question is of questionable taste. There are more elegant ways of using the "Better Work Stories" meme to criticise police than the one chosen. But freedom of speech means freedom for all, even stuff I disagree with).