Default [Q] Screen hypersensitive ?!?

My phone got a broken screen, but I got a replacement device from the insurance.
Trouble is, after a while with screen on the screen seems to become hypersensitive - it's nearly impossible to enter text through the display keyboard or just to zoom and move a webpage
After switching the screen off and back on again immediately it's OK again for a while.

Anyone else seeing this behaviour? I reckon it's a hardware problem, but maybe someone has a different explanation for this problem?

Device: Sony Xperia Z1 (C6903 aka honami)
Recovery: TWRP v2.6.3.0
ROM: SlimKat latest weekly (Android 4.4, CAF stuff included)
Modem: 8974-AAAAANAZQ-10270047-39
Kernel: 3.4.0PIMPED+-gf79222f-dirty

Previous phones: HTC Incredible S (vivo), Samsung Galaxy S3 LTE (i9305)