The schematic had been validated by the ST guys working for the audio device (STw5094A). I don't think that it is so bad. Not perfect, but for sure not as bad as you describe. For sure the loud speaker saturates (it is more a hearphone than a loudspeaker) and the sound output on the loud speaker is poor (I guess it's why it has been disabled on the MP3 application). We tried with larger loudspeaker from the same manufacturer and the result is much better. Now, if you connect the headphone output to an external (PC-audio) audio equipment (PC-loud-speakers), and you launch the MP3 application (from Kasper), you should have a good quality sound (at my side, I don't distinguish between the PC music and the MP3 player running on the Primer).
Jitter could be generated by the regulator. For months, the main issue we are encountering is around the regulators. The L6928D regulators are very sensitive at the input, especially sensistive to ESD peak. The input voltage is limited to 6V max, and small peaks could alter them. It could be that for your primer, one of the regulators (probably U17 in your case) has been already altered. When 'altered', the regulators efficiency is dramatically low, and the regulator consumes half of the current. In such a situation, it would impact the audio signal.