The supposed rise in crime is partly true, I think and partly just their spin of reality. The nature of crime has changed, whereas i.e. the murder rate instead has gone down. People are more prone to report crimes these days as well. On the other hand, gang related crime and outright criminal networks have become a problem moreso than the traditional white biker gang type of mafia and rapes get a lot of media coverage.
What I think though, is that the unchecked privatizations (note here. I like privatizations, but not purely ideologically motivated privatizations) and dismantling of the welfare systems has caused a lot of insecurity and bitterness (while at the same time tax reliefs for all income brackets. . Everybody likes to keep more money, of course).The welfare system is nowadays fairly underfunded Hell, Sweden has one of, if not the most extreme market economy school system there is, where speculative investment corporations own, make profit from and and operate publicly funded schools. Some hospitals and many healh centers are privatized - At a large monetary loss due to purely ideological reasons.
This is where the Sweden Democrats come into play though, because they point the figure on the scape goats - The immigants. Now, the reluctance to admit any problems with integration and immigration has resulted in a) the severity of the issues (which in turn partly constist of regular socio-economic problems) to increase due to lack of action and b) the racist populists to be the face of solving the issues, when they in reality they aren't the answer.