I don't listen to music on my Z, but I do use the media player for radio programs, podcasts, etc. I noticed the problem when listening to Adam Curie's Daily Source Code. You could here clicks and beeps during playback. There was no such problem listening to WBAI's "Off The Hook" though.
My solution was to stop using the media player alltogether and install madplay command line mp3 player. No more pops & whistles, but no gui either.
Another problem with the supplied media player is there is no way to fast forward during playback. Madplay couldn't do this either, so I installed OTR player which uses madplay, provides a GUI, and has fast forward & rewind abilities.
In short, Sharp's included app sucks. Use madplay from the command line for songs, and the OTR player for Radio shows.