Share your experience!
I have the same problem.
Do you know, which display-type you have? JDI or AOU?
There are some people with JDI-displays on Android-Hilfe.de with this issue. So we're thinking, it's related to the type...
I have AUO screen and have also witnessed this issue. Doesn't bother me normally as I don't use Swype-style keyboards. Only time it upset me was when playing Fruit Ninja 
I've got the same problem on my wifes Xperia Z1 Compact and my Xperia Z1...
It was even getting worse since my wife got a cover for her Z1 Compact... Now its not possible to stop alarm in the morning by draging over the stop region because it doesn't react...
She has to lock the screen again, stroke over the screen with her hand, activate again and then to 70% it's possible to stop the alarm...
And it's even there after the update to Android 4.4 (like expected...)
It's become impossible to reliably to input text for me. Seems they've had months to fix this issue. Going to return it tomorrow and stay far away from Sony products.
I removed the dreaded Anti-Shatter-Film last night.
This is obviously a permenant action so I am not *recommedning* it.. but.. the screen hasn't dropped any swipe gestures since then ( ... yet!)
I also have 4.4.2
I returned my Xperia z1 compact yesterday and got my money back.
Together with the department leader of the store we unpacked a brand new phone and tested it with the pre-installed app "Sketch". The new phone is also affected by the touchscreen problem. This leads me to the conclusion that all phones are affected, most users won't realize the issue since they don't use swype as the favorite input method.
If you want to check whether your phone is affected, just open the pre-installed app "sketch" and give it a try. Start drawing spirals or snakes and watch the stroke. Sometimes it happens that the stroke is interrupted, which exactly is the error the defective touchscreen produces. You will probably have to test multiple times in a row until the strokes are interrupted, just try ten times in a row, use the undo button in the app to clear the sketch.
Yes, I call this an error because no other phone I had before had a similar issue and it's extremely annoying when dragging during text input or scrolling.
Here are some images, how the sketches will look like:
I tried the tests as Prao suggests many times over the last couple days, and never once saw an interrupted stroke.
I got a new Z1C because of the touchscreen issue. But the new one also losses the touch time by time (testet in service-menu), but i think, now it is less often.