Factual error: Several of Ragnar's relatives are called "Lothbrok" through the series (most notably, Rollo and Ubba), but Lothbrok was not a family name. The vikings did not use family names at all, though they did use personal sobriquets (such as "Ironside", "the Boneless" or "Finehair"). "Lothbrok" was Ragnar's nickname only. A more appropriate sobriquet for any of his sons would be "Ragnarsson" (son of Ragnar).
Factual error: During this episode, Ragnar is lying down with a half-eaten pear on his chest. That pear is of the variety Conference, it was developed by Thomas Francis Rivers in England in the late 1800s, so almost one thousand years later than the events of the show are supposed to take place (in the 800s). (00:38:00)
Factual error: When Floki lands in Iceland with the other Vikings brought from Kattegat, they land on the beach near Dyrhólaey, the southernmost tip of Iceland. Moments later, they are shown walking near the waterfall of Dettifoss, on the opposing side of Iceland. That is almost 300km (186mi) away, assuming they walked on a straight line across mountains, glaciers, valleys and a highly inhospitable desert in interior Iceland. If they went along the coast, that's more like 625km (390mi). (00:30:55 - 00:31:16)
Factual error: In the scene, Floki walks towards a small waterfall today known as Kvernufoss. Floki is supposed to be the only inhabitant if not the entire Iceland, at least the region, as we are shown no sign of civilisation whatsoever, and as historical record tell us about Iceland in the early 800s (as the events of Vikings seem to take place). But a well beaten footpath is visible, leading to the waterfall at the end of the canyon. That path is an oft-travelled path tourists follow nowadays to reach Kvernufoss, a well-known site in the area. A path like that in Floki's time would simply not have existed (there is nothing in that canyon but that waterfall, no reason to go there if not for sightseeing) and represents a (tiny) intrusion of our modern world in a show set in the middle age Iceland. (00:37:42)
Factual error: When Floki has a vision of Aslaug outside the viking camp along the seine river in France, the vegetation is that of a pine forest and the landscape is that of a mountainous region. There is no such area from the English channel to Paris, which is only flatland. The scene was filmed in Scotland. (00:34:25)