In the case of PiFM, the clock generator is being operated out of spec by a wide margin - it is rated for operation up to 25 MHz, but the code operates it at 100Mhz.

That makes it do some weired things - and I suspect one of those is that when adjusting the clock frequency (by changing the divisors), sometimes it stops oscillating for many microseconds.

Not sure what impact that has in the frequency domain, but I can't imagine it's good...