Hi,
I'm having the same problem as described above, however it seems to be specifically located around the bottom quarter of my screen. It's the apps in the bottom apps bar that keep randomly opening and it's the bottom two lines of my keyboard that I can't type with when it's in its messing about mode.
I have quite a few app updates that I haven't done in a while, could updating these help?
I also haven't updated to iOS 7.1.2 yet, could updating the operating system help, or is there a risk of breaking my phone completely by trying to update whilst the phone is in such a temperamental mood?
Any help greatly appreciated! :)