It started from badge on MAS application icon showing, but MAS tells that there are "No Updates Available". Following suggestion found on the Internets, I have rebuilt the spotlight index.
Now badges are gone, but:
- I still do not have any updates
- All my purchases are listed in "Purchases" tab, with "Install" button by each one - like the apps were not installed, but they are.
- When I click "Install", MAS begins downloading, and label shows "Installed" eventually. But when I close MAS and return, I again see "Install" button, and guess - I am able to download it again. And again.
Some of the apps have newer versions for download. I still get "no updates available".
I googled for answer, but most of time I find folks having same app download from other source preventing it from being updated by MAS. In my case, there are no second copies, no pirated apps, but somehow they do not show as "Installed".