This is more or less what I said (with a lot of "ums" and "ehms" taken out) :
As an immigrant from a European country I cannot talk a lot about my rights being abused, I can however talk about the inconveniences of being an immigrant. A lot of the inconveniences come from difficulties of finding information or finding someone who actually has the correct information. Even employers who employ a lot of immigrants often do not know. I was working in the hospital in Blönduós and after I had seen a lot of workers from the local slaughterhouse who had come to me, but were not insured I called their boss. He was unaware of the fact that according to Icelandic law people (Icelandic and immigrants alike) have to be registered for six months before they have health insurance coverage.
But not only employers, a lot of times people working in relevant institutions cannot answer questions relevant to immigrants.
For example, when I was working on a self-employed basis I had to pay into a private pension fund. As I already pay into a German private pension fund, I thought I might not have to pay into an Icelandic one as well. So I called everyone, from the Icelandic tax office to private pension funds to find the answer. No one could help me until I finally got a foreigner on the phone.
I also worked and lived in Iceland illegally by mistake for almost a year. When I registered in the town hall in Iceland they did not give me the correct registration form (I got the one for Icelandic citizens, not the one for citizens from the EEA/EFTA). Thus I never applied for a residence/work permit. I found out when I did my tax report and after a few calls to the þjóðskrá and directorate for immigration the matter was resolved. And this is where my experience is different from someone outside the EU. For me the reaction was basically "ups, my bad" while someone from outside the EU probably would have been deported.
The distinction between groups immigrants is not only made by institutions, but also by society. A lot of time I am told that I am the "good kind of foreigner". There is a kind of hierarchy on how foreigners are seen in Iceland, with western European on top, followed by eastern European and people from outside the EU, especially people from developing countries on bottom.