I now have a couple servers running Exchange 2010 on Windows 2012, and none of them seem to be able to use the Change Password feature under Options. The page takes a very long time to load the first time, but then eventually goes to a "blank" screen (i.e. the menus and side bar are all still there, and Change Password is highlighted at the top of the screen, but the section where the fields to change the password and the submit button would be is just blank white).
This occurs for administrative and non-administrative users, and seems to be consistent across servers with Win2k12/Ex2k10. Exchange has been upgraded to SP3 in these cases.
I have used EMS to turn off and back on the ChangePasswordEnabled feature of OWA.