This has been happening on my Lumia 920 for quite a while.
Before 8.1: random songs would play in mono with what can only be described as a 'radio static' interference slightly overlaid on top of the song. I would have to skip forward or backwards to the next/previous song, then skip back to the song I wanted... and it would play normally.
After 8.1 upgrade: no longer does the mono + static issue, but instead does random static pops / clicks during random songs. Again, skipping ahead/back, then back to the original song usually fixes this issue.
Does this randomly on all my music. It also does it in different music playing apps, not only / just the official Music / XBox Music.
All my music is on my phone, stored locally, not streaming.
I have never been able to figure out why it does this. Given that it does it in different apps, hardware issue? Haven't really found anyone talking about it online, been very frustrating.