The phone police joke with Johnny is a thing lost on many younger generations. Until the government forced their breakup in 1984, the Bell System/AT&T was a near-absolute monopoly on phone service in the United States whom also owned the phones provided to its customers and were rented out for a monthly fee. It was rumored that if you tampered with a phone in any way (which was prohibited), the "phone police" would come and get you. After the breakup, people could finally purchase their own phones (often from third party companies) and phones were no longer hard-wired into homes.
According to Tim Reid, Grant Tinker personally took him aside to express his concern over the song "She's A Bad Mammer Jammer (She's Built, She's Stacked)" because he believed "Mammer Jammer" was derived from "Motherf***er." Reid feigned ignorance of the connotation.
The song that is playing on the air at the time of the explosion at the transmitter is "She's a Bad Mamma Jamma (She's built, she's stacked)" by Carl Carlton.
Johnny's paranoia about the "Phone Cops" could also be a reference to his counterculture background. In the 1960s and 1970s phone "phreakers" were known to use electronics or even cheap whistles to mimic the tones the phone company used for long distance calls (thus being able to call for free). Some early phone "phreakers" later became prominent in the computer industry, most notably Steve Jobs.