The Mac App store seems to refuse to let you update existing apps if it can't find those applications in the Spotlight index. This affects any user who has turned off Spotlight completely, or has just turned off the indexing of the Applications folder.
This problem has been much discussed on the Apple Support Communities pages and the following solution has been mentioned by several people there (so credit is due to them rather than me).
If Spotlight indexing of your Applications folder is disabled then the 'Updates' tab of the Mac App Store will not list any updates. However, you will see those updates if you click on the 'Purchases' tab. If you try clicking on 'Update' button from this tab, an error message appears indicating that you are not signed into the correct Apple account.
In my case, I only have one account, so this message seemed to be erroneous. I tried signing out and back into my Apple account, but this didn't help. Note that this problem was not fixed by the 10.7.1 update.
Following advice in this Apple Discussion thread
I checked my Spotlight indexing rules and discovered that I had turned off indexing of the Applications folder (see the 'Privacy' tab of the Spotlight preference pane).
Removing the rule on ignoring the Applications folder fixed the problem. I waited until Spotlight could now find all of my applications, and then reopened the Mac App Store and was able to update applications.
This was suggested in the comments to this earlier Xcode updater
hint, and this provides confirmation of that.]