I have the same problem on my 5s with iOS7.0.4. Phone is jailbroken, but I don't think that's going to turn out to be relevant.
Update All is greyed out. Pressing the update button opens an app instead of updating it.
I've changed nothing that I'm aware of to have triggered this problem. Previously, I had things set on automatic updates.
I tried rebooting, resetting all settings, fiddling with the automatic update settings, etc, which did not work.
The apps are actually updated, I think-- the version numbers match the most recent ones on itunes. However if you press on the app name in the update app list page, some apps will still be updatable-- when you get to the page with the full details of the app, and press update there, it sometimes updates (even though the version number is up to date) and sometimes opens the app instead of updating. Updating this way does put a new icon and new blue dot next to it on the springboard. There's a bug doing it this way-- your password is asked when trying to update. That shouldn't happen with iOS7.
The last time the udpates happened correctly was 10/9-- it started 10/10. If everyone else noticed the bug at the same time, it would suggest a problem on Apple's end.