King Aethelred is referred to as Aethelred II. This is a break against the continuity of the original Vikings since Aethelred I was Alfred the Great's brother who never became king.
Harald Sigurdsson (later Harald III or Harald Hardrada) could not have taken part in Canute's invasion of England as he was born around 1016, making him roughly 1 year old at the time Canute was crowned king of England.
The series presents the danish invasion of England by Canute I as a direct reaction to the St. Brice Day Massacre. In reality the direct action was taken by Canute's father Sweyn Forkbeard who launched several punitive raids against England which culminated in a invasion in 1013, over a decade after the massacre.
Olaf Haraldsson did not take part in the danish invasion of England. In fact, he fought on the English side.
Olaf Haraldsson never held the title "jarl".
The show uses the term viking as an ethnic marker, through this is largely a modern phenomenon. At the time "viking" only referred to sea-raiders.
Leif Eriksson and Harald Sigurdsson are shown as being the same age. Leif Eriksson is believed to have been born about 50 years before Harald Sigurdsson.
Earl Godwin is presented as a man in his mid 30's. In reality he would have been around 12 years old when the Danes invaded England and in his late teens when appointed earl, which only happened after Canute took control of England.
Uppsala is shown as located in the middle of a forest in a hilly region. In reality Uppsala is located in farmlands on a plain.
There is no evidence that black Africans, and certainly not Chinese people (as shown in the beginning of the series) were a part of Norse society. It's true that a some Vikings reached North Africa, and a few even as far as Anatolia (Turkey), but they didn't bring locals home and make them Jarls and shield maidens. In fact, their writings at the time show that because of the heat, they didn't even believe it was possible for anyone to live south of the Sahara.