1 try closing 3 apps together, by. Dibble tapping home button, swiping three apps up together with three fingers, the icon in the middle stays on the screen and you can still open it This works on iPhone and iPad
2 on iPhone rename one of your folders,, reboot iPhone, the folder has the same name as before you renamed it, after a reboot.
3 on some third party apps, such as fat notes, make a phone call such as using answer phone, open app and try using it on speaker phone, it won't let you input as you are using phone, I use this for taking notes every day on iOS 6, hopefully this gets fixed.
Last of all, try using reminders, if you used it before as a Callander reminder, it's absolutely rubbish now on iOS 7, I now use apple Callander, should have used it before, maybe it's a good thing as I don't use fat notes or reminders, just Callander
Have you found any bugs yet?