I wanted to post an update, I found a problem with the new App Store yesterday, and while it's not guaranteed to affect everyone, here is what happened, and what I did to fix it.
I'm posting this here because the problem seems to have come from upgrading, so if people here do manage to upgrade, watch out for this issue.
The Problem
App Store doesn't see any updates, even though they are available.
Solution:
Use an uninstall app such as AppCleaner, App Delete, or iTrash
Drag the App Store icon to the uninstaller app Icon, or select App Store with the uninstall app's search function.
Let the uninstaller app find and display the list of all associated files.
From that list, uncheck App Store
uncheck /Library/Application Support/AppStore
everything else is either user specific settings, or caches, so they can be deleted.
After deleting, empty trash, and reboot the Mac.
On restart, open the App Store, and log back in, and you should be good to go.
Hope this helps someone, and it's the only major issue I have encountered since the upgrade. Though in the past, it seems like damaged App Store cache and settings can happen from time to time.
Hopefully this will save someone time from a clean install just by resetting the problem apps.