The first Earl of Kategat is referred to as "Haraldson". In fact, the proper way of addressing a Norseman is by their given name, not the second name which is a patronym. This custom still exists in Iceland today.
The series shows the Uppsala Temple as being located in the mountains. Uppsala was and is located in the Mälaren Valley which does not have any mountains.
In history, Norsemen dressed more extravagantly and possibly notably more sexually provocatively than portrayed in the show. They dressed in bright colors, bathed weekly and used primitive hair-dyes and even came off as vain to some Christians.
King Aella could not have reigned in Northumbria at the time of the Lindisfarne raid, in 793. His reign begun around 863 and ended in 865.
The Viking Age government is shown to be theocratic. In reality, the government of the Viking Era was an elective monarchy. The Norse had the legal and religious right to dispose of their kings which were elected in votes and had the legal right to oppose a royal policy at a thing.
The role of the Seer would have much more likely been held by a woman (a völva) in actual Norse society.
Charlamange is talked about as being dead for quite some time. Charlamange died in 814 and lived to witness the beginning of the age of the Vikings.
At the time the series takes place, Hedeby would have been protected by a large wall, known as Danavirki, to the south.
Earl is used mostly as the title of Norse noblemen rather than the actual title jarl. This is technically not incorrect as earl is a loanword from the old Norse term jarl.
Most historian hold it very likely that the Norse had contact with the Anglo-Saxons in the later part of the 8th century and the existence of England was widely known to them, unlike how they are portrayed in this show. Contact and trade with Anglo-Saxons is actually a likely explanation for the Vikings ability to locate monasteries such as Lindisfarne.
The story says thunder comes from Thor smashing his hammer to the anvil; is invented for the show. in Norse mythology, lightning and the sound of thunder comes from Thor driving his chariot over the sky pulled by two goats, Tanngrisnir and Tanngnjóstr, and throwing his hammer about.
Russia is refereed to in the series, yet name "Russia" did not exist in the period the show takes place. The Norse would have refereed to it as "Garðaríki" (Realm of Farms). In fact, the most widely held theory of the origin of of the word "Russia" is that it came from vikings native to Roslagen, in Sweden, who became rulers in the area.
The historical events and characters associated with the legends of Ragnar Lothbrok and his sons took place in the mid to late 9th century. In fact, most of the events and character in Vikings, happen 50 to 90 years to early from their possible historical root.
Rosaries can be seen on some monks even though the rosary did not first appear until about four centuries after the main time frame.
The first Viking-attack on Paris did not occur until the 844.
Thorstein frequently wears a brigandine, which where not introduced in Europe until the 14th century.
Athelstan is often seen with a cloak held together by strings and wearing a pin on the coat. The purpose of this pin is actually to hold a cloak together so wearing it a coat with strings is superfluous.
Kattegat seemingly is located in Norway, yet people are show riding between Kattegat and Hedeby, despite the later being located in southern Denmark and there being no land-connection between greater Scandinavia and the danish mainland until a 1000 years later.
The whole time line is quite mixed up for the series. At the time of Lindisfarne (S01), Ragnar wasn't even born. King Ecbert died about 6 years before Ragnar, in 839. Aethelwulf would have been king at that time. Aethelwulf himself died in 858, 7 years before the invasion of the Great Heathen Army. In the series, the invasion seems to follow Ragnar's death almost immediately, while in reality there was a 20 year gap between both (his sons - with the exception of Bjorn - being young children when he died). Season 4 also shows the winter at Repton as if it were immediately after landing in England, while in reality it was 8 or 9 years after the invasion. Ecbert (who is shown as king of Wessex) and his son Aethelwulf were long dead. Also the successive kings Aethelbald, Aethelberht and Aethelred (sons of Aethelwulf) were dead. King at the time of Repton would have been Alfred, Athelwulf's youngest son, about 24 years old. Not a child as shown in the series.
The Saxons and the Danes do not seem to understand each other at all. In reality Saxon and Old Danish are closely related Languages. It should be fairly easy to communicate, like modern Swedes and Danes.
The term "Sweden" and "Svealand" are used interchangeably. The term "Sweden" is a 17th Dutch loanword and prior, Sweden was called "Swedeland", a literal translation of Svealand, or "Sweotheod"/"Svithjoth" (Swedepeople).
Gotaland/Götaland seems to be located high up in the mountains. Through a large part of Götaland is covered by hilly highlands, the highest peak in Götaland is 362 meters.
Borg is portrayed as being seen as unstable by his peers for communicating and asking the skull of his dead wife for advise. But in pre-christian Scandinavia, there was an extensive cult of the dead and communicating with the dead and even interacting with them was common. Modern ethnic groups like the Torajan people still has such practices. There are even myths of Odin communicating with the head of his dead teacher, Mimir, so Borg's action would not have been seen a deviant behaviour by Norse pagans.
King Harald is mentioned several times as being the king of Tamdrup. The historical Harald was king of Vestfold which is in southern Norway. Tamdrup is located in Denmark and Harald held no Danish domains.
Ragnar Lothbrok's sons are referred as "Bjorn Lothbrok", "Ivar Lothbrok", etc. However, Lothbrok is a nickname (meaning "shaggy breeches"), not a family name. The sons should properly be referred to as "Bjorn Ragnarsson" (i.e. son of Ragnar), etc. Family names where not used in Scandinavia at that time and did not become common until 17th century and not the standard until the 19th.
Hedeby is shown as being located in the hills, as opposed to a sea side trading town surrounded by swamps and farmlands. Also, Hedeby was located in the south of modern Denmark, which highest peak is about 172 meters.
There are quite a few modern phrases used throughout, most notably "shut your face," a fairly recent derivation of the more widely known "shut up," first recorded use being in 1857, more than a thousand years after events depicted.
Judith was the second wife of Aethelwulf, and wasn't the mother of any of his children, including Alfred. She was the daughter of the King of France, not Northumbria. And he was king of Wessex when he married her; she never knew her father-in-law Ecbert/Egbert.
Halfdan the Black and Harald Finehair where not actually brothers, but father and son.
The soldiers of Wessex are wearing helmets of a period 700 years later than depicted in the story. These are burgonets of an Italian style, more at home in Renaissance Florence than England. Moreover, the kite shield was not introduced into England until c.1000, just before the Norman invasion. Other English troops are seen wearing padded leather jerkins of 1200/1300s, so are also completely out of period. The Swedes are seen wearing helmets used by Anglo-Saxons in the 8th century, not by Swedes.
The things are shown to take place in earl Haraldson's hall, rather than a more public and open air meeting place. In later seasons they do take place outside in a public place, though.