There is a very common touchscreen bug with the Oneplus One that can only be partly/temporarily fixed by a reboot and shows in several ways:
Although this seems to be in some way related to the hardware (because I could easily reproduce it by making it warmer), a new touchscreen firmware was published recently in the CyanogenMod 12.1 repository that seems to work arround the problem somehow. I can attest that installing the new firmware fixed the problem on two Oneplus Ones that I tried it on. Battery life is noticably worse though, but this is said to be fixed with some changes that were committed to the CM12.1 repository on June 2.
I installed the new firmware on my phone with CM12 (YNG1TAS17L) by flashing Franco kernel R43. To do this, reboot into the bootloader and flash the boot.img with
fastboot flash boot boot.img
Here is an extensive post about unlocking the Oneplus One and flashing things.
Update August 02, 2015
The touchscreen problems are now fixed in the official and current version of CM12. Battery life is as good as it was before flashing the custom kernel.