We have open mikes all the time, and have heard what we decided was (with a 99% probability) someone getting it on. If no one misses a call because of it and the act isn't some sort of 'I can help you out with that ticket' thing, the brass doesn't say anything. Besides, between dispatchers leaving their foot on the pedal and commenting on how bloody the movie on the tv is and my shifts cursing on air*, the 911 director has bigger issues to worry about.
*In the past year, my sgt has gone on the radio and said 'I'll be out with some jacka-- spinning doughnuts in the school parking lot' and '15 Lincoln Dispatch, traffic. Be a gray in col... What the hell are you doing, dumba--?' while I apparently don't let go of my shoulder mic quick enough when in a foot chase so 'Get the f--- on the ground!', 'I'm faster then than you, motherf---er!', and 'I'll taze you in the back, b----!' have graced all of those innocent ears in scanner land.