He made some claims about the schengen directive about what responsibilities of travel companies have that did not really hold water. Also, he repeatedly confused migrant with refugee(classic beginner mistake).
However he started to nuance his critique later and came to unpopular opinion that the Swedish migration system is severely flawed.
Government of Sweden uses funds that is budgeted to foreign aid to pay for immigration. Biggest receiver of Swedish foreign aid is a Swedish county (yes, true).
Using foreign aid to fund immigration is something done both by the political parties of the right and the left.
Rosling said that using foreign aid money for expenses at home is just wrong. Foreign aid should go to regions in distress. Funds for immigration should be taken from other less important areas and/or increased taxes.
At this time almost only the Swedendemocrats(controversal anti-immigration party)criticized the migration system with basically the same argument, help migrants/refugees at their home region. Help many more at a cheaper cost (Sweden is expensive).
At this time in Swedish politics all of the other political parties tried to boycott the Swedendemocrats with the infamous December treaty (basically a pact to block elected members of parlament from the Swedendemocrats to have a say in any question).
To have a very famous and popular personality with a huge cult following say this during this time of Swedish history didn't go well at all with the establishment and he was less and less seen in public debates.
Rosling was of course not a Swedendemocrat, he was a liberal (European definition) and probably did not agree much with Swedendemocrats in other issues except foreign aid. However in todays debate climate where you have to buy everyone's opinion wholesale this didn't work so well for him.
Rest in peace Hans. You did fantastic work with your studies on poverty and global health. Farväl.