Ubuntu 16.04 LTS clearly is not ready for prime time.
First problem I encountered is that I could no longer login using x2go making graphical administration remotely impossible.
Second problem is Apache wedged after a few hours of operation and would not restart until I rebooted the machine. That might be acceptable behavior for Windows servers but not for Linux.
I’ve reverted our web server back to Ubuntu 15.10 for now using the image I made prior to starting the upgrade process.
It’s unfortunate because php7 did shave several hundred milliseconds off of the load time for our home page so it really did provide substantial speed improvements.
I may attempt an install of php7 independent of an entire operating system upgrade.