Put this here in case you'd consider it spoilers... But, in the actual story, Ragnar had no children with Lagertha and that's one of the things that bothered me the most...
Bjorn Ironside was a child he MAY have had with Aslaug, it is believed Ragnar may have only been his step-father, but it is not fully known.
Ragnar had TWO sons before meeting Aslaug, Eric and Agnar, mothered by Thora, who has not been mentioned in the show... So, if they tell the full tale of his life, I'm not sure how they'll explain the 2 sons as they had an important play in his death - They were killed by Ragnar's appointed ruler of sweden and Ragnar's other children decided to get revenge, and they did. Ragnar didn't want to be overshadowed by his children, so attempted to conquer england, where he was finally defeated after being one of the biggest, baddest king/pillager to ever exist. Perhaps Ragnar wouldn't have tried to conquer something so large with so few men had Eric and Agnar not been killed.
Ragnar and Aslaug had four children, it is believed that Bjorn is the eldest (IF he was Ragnar's son), Ivar the Boneless, Hvitserk and Sigurd Snake-in-the-Eye. Ivar the Boneless is displayed in the show to have no bones in his legs... That is ONE theory, but is not the most popular... As he was a mighty pillager and great warrior it is believed the name Boneless came from his great ability in battle, to move "as if without bones". Not due to the actual lack of them... It's going to be hard for the show to explain that as well, for he's going to have a hard time swinging an axe if he can't even stand.
And Sigurd had just been born when I quit watching it... So I don't have anything to say about him, and Hvitserk hasn't been born yet, and may possibly be just another person they pretend never existed...
Some of the rituals and spoken beliefs of the Gods are a little questionable as well... But I just personally don't agree with it, even back then there were many ways the religion was followed and believed in, so just because it doesn't match my personal beliefs as a Nordic Pagan doesn't mean it's historically inaccurate...