I own a Xperia S (so you will ask why do I post in this topic for the Z1 - I'd like to buy this phone in a few weeks) and I've also this touch screen problem.. So I don't think it is Z1-related, and Z1s might be concerned (xperia s : beggining of 2012, xperia z1 mi 2013.. Bravo Sony!), but I don't hope !
@ghostman2 : So after the 3rd replacement you got a fully-working touchscreen ? That's better than nothing, but they could have fixed the problem 1st time.
I really wanted to buy this phone, but if the problem is still persisting..