Maybe other people thought Trump's comment came out of left field, but I was certainly aware of the problems they are having in Scandinavia, especially Sweden. I have a son who has lived in Norway the last five years, who is very aware of immigrants arriving and causing problems from the very beginning. Chris is an immigrant himself - doubly an immigrant actually, having come to New Hampshire at age 13 and moving to Norway after he got out of the USMC. Thus, he compares his own behavior and work ethic with theirs, not to their advantage. He is probably too easily irritated and jumping to conclusions when he talks about them arriving at the bus terminal and harassing the women or demanding apartments immediately, but his aren't the only reports. And he is way, way up north in Tromso, where they are only beginning to have large numbers of immigrants.
Also, I am of Swedish extraction on one side, so I have kept half an eye on what is happening there since childhood. That has brought me in contact with websites that report what it is apparently not allowed to be reported in Sweden. (See Staffan on my sidebar, for example. Or catch up on Hjernevask, the Norwegian 7-part series about inheritance and behavior. There are subtitles, don't panic.) Crime statistics are not broken down by whether they are committed by natives or immigrants, and in the second generation you get classified as a native anyway. But you can look at the cities that have had more immigration and compare crime rates, using only arithmetic. Thus, Malmo, right down on the southern tip and across from Copenhagen, now has a school population that is 52% 1st or 2nd generation immigrant. Coincidentally, this is where the bombs are going off. Very unSwedish.
Conservatives, especially religious conservatives, are prone to attributing this to Islam. I am not so convinced of this. Yes, I have read many of the quotes from the Koran about how observant Muslims are supposed to act toward the infidels and the rest of the world. But not all one billion Muslims seem to be putting much energy into obeying those particular passages. Certainly the terrorist attacks usually have some element of Islamic rhetoric. But the crime and general violence I think is simply primitive. For those who follow Pinker's subtext in The Better Angels of Our Nature, it is one specific area of the world that has low intracultural violence, while everyone else has higher (sometimes much higher) rates. There's that Hajnal Line again. It is lack of violence which should surprise us, not violence. If anything, I think that Islam has been a moderating influence on the deeply tribal Middle-East. Not enough, but some.