Apple has just released the OS X 10.8.3 update for Mountain Lion users, and while the update has gone smoothly for most people, as with any update there are a few who have run into a couple of hurdles when installing.
The most prominent issue so far is a small number of users have run into an issue where the update appears to install but then gives a message that simply states "Update Failed" with an option to restart the system. Upon doing so, the system reports it is still running OS X 10.8.2; however, subsequent attempts to update result in the App Store crashing.
If you find yourself in this situation, the first step is to try clearing the App Store cache of any downloaded files to see if that is what is causing the program to crash. To do this, open the Terminal utility and run the following command to load the system's caches directory:
In the Finder window that appears, locate the folder called "com.apple.appstore" and remove it, followed by relaunching the application, which should hopefully now launch successfully.
Now you have the option of trying the update again, or you can try downloading the Combo updater for OS X 10.8.3 and applying it manually, the difference being the Combo contains all files changed since OS X 10.8.0 whereas the Software Update service on the system only grabs the files your system needs from the version of OS X it currently has installed, so it may not replace a file or two that could be lending to the problem at hand.
If the Combo updater will still not install, try running a general maintenance routine on your system to clear system caches, check hard-drive setups, and manage other temporary configurations that might be contributing to the problems you are experiencing, followed by updating again.
Finally, if nothing else works then you should be able to fix the situation by reinstalling OS X and updating the fresh OS installation. Reinstalling will only replace the operating system software underneath your user data, applications, and account settings so it should not affect your workflow. To do this, reboot your system with the Command-R keys held to load the OS X Recovery Tools. Then choose the reinstall option and follow the onscreen instructions to download and apply a fresh copy of Mountain Lion to your system. After this is finished you should have an earlier version of OS X installed, and you can then run Software Update or apply the Combo updater to get it up to date.
These steps may also help those experiencing any other issues with the latest OS X update. Keep in mind that if you use Boot Camp with the latest update and are experiencing some problems with your Windows installations, then be sure to update the Boot Camp drivers for that with Apple's Software Update service in Windows.