How do you file a bug report for Windows?

There's no submit a bug report option directly. The way you do it is to call Microsoft Support and open a support request(can also be done online). If they can reproduce your issue and verify that it's actually a bug in WMP 12 they will file a bug report.

Be prepared to go through all troubleshooting steps they will have you perform, otherwise it will most likely never be reported as a bug.

This is where I have reported bugs in .NET, and it SEEMS to be for other products as well: http://connect.microsoft.com/

Edit: Just checked and there ARE bug reports for Media Player there (do a search), so that does look like what you're looking for.