After downloading, and upgrading to OS X Mountain Lion, the Mac App Store shows a "download" link for it; it doesn't show "installed." Secondly, although I have downloaded it twice, it does not show between my applications.
Why does this happen?
When you purchase Mountain Lion in the App Store, it will first download an application called
After that Mountain Lion installs and reboots into your Mountain Lion install. The installer application will be automatically removed - because most users won't need it anymore.
If you open the App Store, you're offered you to re-download Mountain Lion (hence the button says "download"), which could be useful if you wanted to create an install USB with the
You can verify if you have installed Mountain Lion by going to the menubar and click: Apple icon → About this Mac. In case you have Mountain Lion installed, you'll see this: