Organic Groups module  messes up node editing
Just figured out that the problem was not caused by the references module, but by the "Organic Groups" (og) module. It seems to be a known bug in the organic groups module that basically hides/disables all fields for custom content types that are not marked as group or something like that. There's a report about this in http://drupal.org/node/1029230.  

Disabling the organic module make the fields come back again, and even relationships seems to be editable again. I can live without organic groups for now, and considering the severity of the bug I will definitively not try to use that module again until it has been fixed.