If my outlet tester reads OPEN GROUND and or HOT/NEUTRAL REVERSE is that a serious safety issue?

I live in a NYC apartment building. The other day or fridge outlet died. The 3 light outlet test just read lite up RED only. I decided to test other outlets and many of them read HOT/NEUTRAL REVERSE and one reads OPEN GROUND. How serious is this? Should I report the building to DOB if they refuse to address it?