HT1338: OS X: Updating OS X and Mac App Store appsLearn about OS X: Updating OS X and Mac App Store apps
The Original Poster states they are using OS X 10.8.2 despite posting in the Lion (OS X 10.7.x) area.
Could you be specific about which OS version you are running and which Updates are listed in the App Store > Updates that don't appear to work ?
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
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