Hi,
The issue seems to be that in the Apple Menu > About this Mac it does actually say it has updated to OS X 10.8.3 and that a temporary folder that is supposed to be cleared at the end remains suggesting the Install has not finished and subsequently the App Store alerts you to an Update again.
To actually quote the contents of the link I made earlier.
It turns out what happened was the 'cleanup' portion on the update to 10.8.2 never executed.
It had left a hidden directory in /Users/Shared/ named .mtnlion - this directory contained the installer/updater app that kept coming up on the dock when first booting up.
I opened the console and went to root using sudo su - then used ls -la /Users/Shared/ to show the hidden directories, sure enough the .mtnlion directory was there.
Once I deleted this directory using rm -Rf I rebooted and the updater was no longer on the dock and did not prompt for an update.
Hopefully, this will be helpful if anyone else runs into this problem.
8:00 PM Saturday; April 6, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously