Okay, on my iPhone 5, when I open some apps, they just close immediately. The solution to this is to update the app.
When I go to the App Store and click "update" on the list of "Updates", the app opens
And immediately crashes.
Which is to say, it doesn't update, it just crashes. App Store doesn't help, because it's not downloading the new version, it's just opening the app.
So, how does one update an app when the App Store just opens the app?
Instead of clicking "Update" in the list of updates, search the App Store for the app, by name, using the search functionality.
When you find the app, tap the "Open" button. That'll either download the update or give you a screen where you have another update button. Tapping that update button will download the update.
Unless the App Store doesn't have the update at all. In that case, you might have to upgrade your phone or ipad.
Which is to say, they will be prying iOS 6 out of my cold, dead hands.