Seconded. As well as a "Check for Updates" section.
It doesn't actually need a "Check for Updates" button, just something that says you're up-to-date and an "Update" button if you aren't up-to-date.
Only being able to update from the notifications makes me feel viscerally uncomfortable. I got the same "Update failed" notification, and the "Click to update" notification was gone. I don't like that. I thought notifications were supposed to persist in the archive/history...