It came to the point where I changed operator to see if that would do any difference... and it did! I hate to admit that.
When I confronted the earlier operator with this, they told me they talked to Apple about the problem, but either of them could solve the problem.
I then asked them if they would try to use another operators carrier profile as some sort of template, to see if that made any difference... I don´t know if they did this. It´s just my thoughts about this problem.
If it helps anyone reading this thread, I live in Norway and used Onecall (pinned to Telenor as network), but then switched to Djuice, which is "fullfledged" Telenor network and uses another carrier profile than Onecall. That solved the problem for me. When I some time get my hands on iPhone 5, I´ll try going back to Onecall once more to see if anything has changed...