My 2 cents:
police officers are public servants. They represent & enforce the law of the city, county or state in which they serve.
Aside from the gun & physical altercation, I find it highly inappropriate for any public servant to use profanity while executing their duties. Trust me, I'm not a prude. I love a foul mouth when the setting is appropriate. However, think about what would happen to you at your workplace if you spoke to a colleague or customer with that language--or even had a potty mouth in everyday conversation. You'd be hauled into HR and warned. Most workplaces have polices against obscene or profane subject matter (hence the NSFW warnings on forum discussion). this officer was AT WORK. He used filthy and descriptive profanity to MINORS. What would happen to any of us if we just unleashed profanity on minors we didn't know in a public place?
more notably, what would happen to any of US if we used that kind of language on an officer who pulled us over? Try saying "f*ck" or "goddamn" or "ass" to an officer and see what happens. Some states (like IL) even have finable laws on the books for "verbal assault" that cops and judges like to use when they're involved in road rage incidents while off duty (it's been in the news before... judge threw the book at a guy who flipped him off).
its a double standard. I've seen cops in my city detain and scream at teenagers for nothing more than using profanity among themselves on a public sidewalk and this asshole cop sat them all down on the curb & chewed them out for 5 minutes (oh yes... AND asked for their IDs. Hello 4th Amendment?)
I lose more and more respect for police every day. I know the whole "few bad apples" cliche, but I personally know a few cops and they're all just generally very sour asshole type-A people--kinda like the worst among the JW elders. That control-freak hot-tempered attitude is in every profession but not everyone gets to carry a side arm and ruin people's lives.