Annabel - After successfully updating, the app will still show an Update button, but will be listed below the heading "Updated October nn, 2014". Just ignore those.
Once again, for anyone who is still having the problem:
Work Around:
Search the App Store for the app to be updated. You can use the search box at the top right of the update screen.
Tap the details for the app. That should give you an update button. If it opens the app instead, close it and do the same thing again. If you are asked to verify your account, that means you paid for the app. Do the verify procedure until you are asked to pay for the app. Then cancel. Do the update routine again, and you will be notified that the update is free, since you have already paid. I found that once I verified one paid app, I did not have to do any of the others.
When the update has begun, you can go back to your update list and do the next, etc.
If search does not bring up your app in the store, google for it like this "Name-of-app app itunes store". Click the link that has that string in it and it will take you right to the correct app in the store.