Unexpected error when installing OS update in OS X
The Console.app found in the Application -> Utilities folder (or Other folder in Launchpad)  gives you access to the logs for the machine.

Under /var/log, the file named install.log (and any variants named install.log.x.bz2) will give you the information about the last install.

Note the files named install.log.x.bz2  are older versions of the same file created duting a process called rolled over when the file size of the current install.log file reaches 1000K

You need to search your install.log for the string "OSXUpd10.8.2Supp.pkg" which will give you an idea of what happened during your install.

Update: From your log file, it would appear that your have a Kernel Extension that is causing this issue.  Either it has a permissions problem, or is somehow causing this annoying issue.

can you paste this line into Terminal, and post the results?

kextstat -kl | awk ' !/apple/ { print $6 $7 } '


Update 2: This would appear to be at least a trial and error solution. There are multiple threads on the Apple Support forums, from installing 10.8.2 to installing Xcode.  Each one has different people each having issues with different kernel extensions that when removed resolved their issues.

I'm afraid I don't have any way to determine which of your kernel extensions is the cause; someone else may be able to shed more light.  I would however expect the Virtual Box and Parallels extensions to be fine, not the least since I have them both also, but that this issue would be more widespread if they were the issue.

Finally: the manual for kextcache advises that using the touch command on /System/Library/Extensions/ forces the kext cache to be rebuilt.  You could use this as a method to determine which kext is causing the issue by uninstaling each in turn, performing the cache update and checking the logs to see if the cache was updated successfully.