Preinstalled Mountain Lion and iWork is not found for Updates
There is no way to make App Store output debugging info, all debugging info is that what you see in the Console logs.

App Store doesn’t “detect” that it is on Mountain Lion. Mountain Lion 10.8.0 ships with a different version of App Store that is unique to that version. In addition to this, App Store may check the SystemVersion.plist file to determine on which version it is running.

iWork and Mountain Lion don’t appear in the Purchased tab of App Store, because you did not purchase them through the App Store.

As for the App Store not detecting the 10.8.1 update, that is a problem even I have had (With Xcode, though). About 3 days after the update disappeared, it reappeared. I never found out the cause of the problem.