What is disadvantage of frequency jittering?

[grizedale]

Some pwm controllers make the switching frequency vary 5KHz around the standard switching frequency so as to improve conducted emissions.

..EG TOPswitch by powerint.com

But what are disadvantages of such frequency jittering?

 

[emontllo]

I have worked with VIPER17 and the jitter may cause a little output voltage ripple (at the jittering frequency) if the control loop is not properly adjusted.
This happens in a flyback converter operating in discontinuous mode, since the output power depends on switching frequency and therefore the control loop has to compensate this variation.

According to AN2753 from ST:

The VIPer17 internal oscillator gives a switching frequency modulated by a triangular waveform of 250 Hz (typ.). The power demand of the load is constant, but,
due to the variable switching frequency, the power delivered is not constant if IPK is constant.
The control loop reacts to the unsteady switching frequency, modulating the feedback pin voltage and then, the drain peak current.