The problem comes from the recent wave and semi-open borders within EU that make it easy for some mafias to move into the country to commit crime. It's a tought problem.
I met a group of young, liberal, well-educated Danes on a trip to Japan once and later, accepted their invitation to visit Denmark, where I stayed for about ten days.
Make no mistake - these were picture-perfect Copenhagen Danes with exactly the liberal and progressive bent that you would expect and they were quite well educated and relatively wealthy (one of them even had a car!).
These people did not beat around the bush: they can't stand "the turks", they don't understand why they are there or why they behave the way they do and they cannot believe that their society has been infiltrated in this way.
It wasn't hateful, or even racist per se ... just a very pragmatic rejection of events.
This was in 2004 - I can't imagine they feel any better now.
Of course, in his eyes he was not an immigrant, but an expatriate.
A little of effort trying to understand others can make wonders. Most immigrants behave, a few not. Of those, a few are just bad persons, but most are just poor an uneducated and probably they would prefer to be in their home countries.
If immigrants are so problematic, maybe we should be looking into what, in many cases, our governments are doing (or not doing) in their native countries.
Both left and right leaning governments have failed to implement good integration policies. The parties on the left have been to naive and assume that things would naturally work them selves out: They trusted that the people coming into the country would want to learn the language, integrate and become Danes. On the right the opposite was assume, that the policies should be to not let people feel welcome, in the hope that they would leave.
Troublesome groups are let in, because Denmark is legally required to. But the evaporation of trust in others isn't purely an immigration issue, it happens between Dane as well, and that's worse because we're not entirely sure why it's happening.
Unfortunately we've had a series of governments with increasingly bad integration policies, leading to ghettoes and increased friction.