Touch lags in all apps, except keyboard I've noticed a delay of about a quarter of a second between tapping the screen and the app responding. Thud happens in all apps - it's most obvious in the game "aa", a fast, reflex-based game which is essentially unplayable with so much lag. The lag is also clearly visible in CyanogenMod's calculator app, where it clearly can't be attributed to complex or expensive rendering.

The only place I don't see the lag is the keyboard - keypresses register instantly. 

Rebooting the phone in safe mode does not solve the problem.
I figured out the cause as I was writing the question - the "triple tap to zoom" accessibility feature was enabled. This means that the phone can't register any taps until waiting to make sure there isn't another tap.

Disabling this feature removed the delay.