I just called GoDaddy support and I was told Import Zone File function is broken and no ETA on when it will be fixed.

 

To reproduce:  it doesn't matter what domain name we have, you simply go to "DNS Management", go to "Advanced Feature", then export your current zone file (either Windows or Unix version/format, doesn't matter) to your Desktop, then immediately click "Import Zone File" and select the file you just saved, you simply get an "Error" message.