There is a Windows Update troubleshooter in Control Panel-Troubleshooters, have you tried that to see if it will give you any more info?
How do you know .mum and .cat are corrupted?
The WindowsUpdate.log in the Windows directory keeps tracks of updates and might you some cluses as to what is happening. Do a search for that KB or go to the last day if you did an update.
I search my 32 bit install and see around 35 .mum package files for that KB plus a update.mum and update-bf.mum - information only, just in case.
Have you tried opening an administrative command prompt and type sfc /scannow to run a system file check. Maybe that would straighten out the corruption.