I doubt any existing problems for the 2012 Nexus will be solved; isn't 5.1.1 the last official update it received?
In any case, I got the tablet not too long ago to replacing my aging PlayBook. I like it. I updated to 4.4.4 and didn't go beyond that for awhile. Was happy I did, based on reports about Lollipop's questionable performance.
I recently decided to unlock mine and install a custom rom, to have a newer OS, (hopefully) better security, and some optimization. I went with XenonHD (Lollipop based), and I'm glad I did. The N7 runs like a champ on this rom. The process is pretty straightforward with the Nexus Rom Toolkit. Worth a shot!