My apps are all Apple - no third party apps. On my wife's ipad mini there are programs which now opened cannot be dismissed. I am sure someone can explain the advantages to upgrading but it seems to me so far the upgrade is mainly cosmetic and has just introduced a load of problems. I wish I had not upgraded although I suspect long term there will be no choice.
You should look for and install the App updates for iOS7. That will fix most of the failing apps.