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I also have the same problem the phone's touchscreen don't work on flat surface and also when I hold it in my hands touchscreen works 3/4. when I turn on glove mode, then turn off the problem is solved for one day, after a day the problem returns. I think than it is a software problem. I am on 4.1.2, which android version do you have on your xperia sp?
I think android 4.3 will solve this problem 
I'm using 4.1.2...because for me .205 update there isn't yet and I don't any intention to update to .266...
p.s. sorry for my english 
I heven't updated it yet :D, I heard that viber isn't working in .205 
I contacted Sony support via email and he answered that it is a hardware problem 
The poor touch response is down to not holding the phone - nothing to do with a flat surface!
Capacitive touchscreen displays rely on the electrical properties of the human body to detect when and where on a display the user touches. Because of this, capacitive displays can be controlled with very light touches of a finger and generally cannot be used with a mechanical stylus or a gloved hand.
OK so I stole that definition from the web, but it's the reason the phone doesn't respond when it's on a flat surface.
Dave