While I'm not a Swede I do live in Sweden and I do follow Swedish news (both the 'official' as well as the 'alternative' sources). I do have to concede that SVT (and, more or less to the same extent, SR - Swedish Radio) has a problem with bias. Being a state-financed broadcaster (through a mandatory payment for anyone who has 'television reception equipment' in their residence, no matter whether that equipment is used to watch SVT) they are by law mandated to be politically neutral. This is something they (as an organisation) fail in, and rather miserably. If I were to place them somewhere in the political spectrum they would end up next to the (ruling) labour party, sometimes to the left of them, sometimes to the right. In this they mirror most of the 'official' media in Sweden which hover around the same area in their political orientation. As the previous poster indicated this can partly be explained by looking at the political orientation for the large majority of those employed in the 'media' and 'culture' sector.
This combination of left-oriented media and a left-wing government has led to a systematic failure of the media to keep check on the government, especially where it concerns Miljöpartiet (the green party). That party was recently shaken by a number of scandals, mostly related to the infiltration of islamist politicians - one of whom made it as far as a position as minister for housing in the current government, he stepped down when his position become untenable - with an agenda which diametrically opposed that of the party itself. Until a few months ago there was not a single (!) critical voice in the 'official' media where it concerned this party. Where all other parties - especially those which are in opposition against the current migration policy in Sweden - were targeted by the media (as they should be, this is part of their function, to keep check on the political establish ment) the green party sailed by without a single critical voice.
Another problem lies in the fact that Swedish media often use supposedly objective but in truth politically activist research organisations as source for their material. The best example of this is 'Expo', an organisation which was set up to do research on anti-Semitism, racism and xenophobia. This might have been their charter once but they do not live up to it, instead they are a political activist organisation with an agenda which resembles that of Vänsterpartiet ('the left party', formerly known as 'Vänsterpartiet Kommunisterna' or 'the left wing party communists', they changed their name after the demise of the Soviet Union) and Miljöpartiet. While in itself this is not a problem, they are still treated by the media as if they are an objective, politically neutral organisation. That is a problem.