On my Nexus 4 (Lollpop), the nav keys no longer respond when it is in portrait mode, and the q key no longer responds when it is in landscape mode. Here is the bug report. This has been discussed at the Google Group, and Grigoriy Kraynov has brilliantly put together an unofficial fix, but it requires rooting the Android. (Correction: Maybe not rooting it, but definitely some dangerous digging around in the OS's innards.)
There are also occasionally ghost presses. (I configured my phone to show a white dot when there is a press, and sometimes there are a lot of them all together, usually in this malfunctioning area, without my pressing the screen.)
It's been called a hardware bug in the digitizer, but it looks to me like it's in the software layer -- why would one particular rectangle stop working?
Can anyone suggest a simpler way to fix this? It's hard to believe that Google would allow such a significant bug to go unfixed.
My workaround is to install the Button Savior Non Root app and an autorotator app (to enable 4-way rotate in every app). This workaround is more or less OK.