A server I was working on refused to let me update it through Windows/Microsoft Update. It would tell me that the computer needed an update before I could update it (!). First it would download some files from the Microsoft Update site, copy them and, finally, try to register them. This last step reached 100 %, but always terminated with the error 0x8024D007.
Process Monitor revealed that regsvr32.exe was called several times and the it failed with an Access Denied error on the registry key HKEY_LOCAL_MACHINESOFTWAREMicrosoftWindows NTCurrentVersionSvcHost. Looking at the permissions on that key I saw that the local Administrators group only had Read access. I changed it to Full Control and was able to restore Windows Update functionality.
In my search for a solution this particular scenario never showed up, so maybe this will help someone.