So apparently the 30GB Zune player can't handle the "random" events in the global calendar- leap years. So to "correct" this issue, the solution is to wait and let it solve itself. Apparently Zune owners were to let the battery die, leave it off and don't turn it on until fully charged.
And just for fun, here's the FAQs (from ZuneInsider) regarding said problem, with my translated answers:
Q: Why is this issue isolated to the Zune 30 device?
Because we didn't want to use the same drivers in all Zune products. That would be dumb.
Q: What fixes or patches are you putting in place to resolve this situation?
Nothing. We're all on vacation until the 5th. The problem won't be around then.
Q: What’s the timeline on a fix?
It will fix itself. Because here at Microsoft we create self-aware software.
Q: Why did this occur at precisely 12:01 a.m. on December 31, 2008?
Because the concept of leap years is completely foreign to us.
Q: What is Zune doing to fix this issue?
The nanorobots that act as microscopic DJs within your Zune are working feverishly to repair the issue before the end of the year.
Q: Are you sure that this won’t happen to all 80, 120 or other flash devices?
Because we made it. Should have spent the ca-ching and bought the larger devices.
Q: How many 30GB Zune devices are affected? How many Zune 30GB devices were sold?
All of them. While quantity of Zune devices sold are not broken down by model, it is safe to say there are more 30GB Zune devices sold than Yugos produced today.
Q: Will you update the firmware before the next leap year (2012)?
Yes, we always update firmware. Duh. Will the update include a solution to the problem? Probably not.