I don't think the issue is that its giving the Police departments 's bad publicity, its that the show is making the communities look like shitholes. This is focusing on the part of towns that most of the viewers stay out of. I never saw the episodes that were in Tulsa, but my GF commented that she didn't know that Tulsa was that dirty/crime ridden, and she's lived here 15+ years. Mayors and community politicians are probably telling police departments to stop the show because its making the politicians look inept.
I think the PD's have come across really well and its been good for them. I often wonder when watching if these officers usually let guys go as often as they do when cameras are rolling though. Couple weeks ago they showed a woman driving her kid around at night high on MJ. Officer was like, well I cant let you drive home, but you can call your family to come drive you home. No ticket or anything. Justin Blackmon probably watches this show and wonders where those officers where when he got pulled over for weed ;-)