The compatibility checker is a spin-off from bug 115291 and known from Microsoft. http://technastic.com/wp-content/uploads/2016/02/Microsoft-Word-Compatibility-checker.jpg
The idea is to tell the user what potential issues it has when saving in the chosen file format (long list for plain text, reasonable info for docx)
Would be very useful I think => NEW
I think many people will be against this, e.g. see bug 59346 comment 2.