While their hairstyle might be regarded as a very rough modern adaptation of the middle of the 11th century Normans, depicted in the famous Bayeux Tapestry, /u/Searocksandtrees commented (based on the interview article of the producers) in Is the History Channel's "Vikings" accurate with regards to hairstyles? that at least Ragnar's hairstyle was invented on spot.

As for Bayeux Tapestry, Comparison between the hairstyle of Harold Godwinsson (center-left) and those of other Normans in this scene of the tapestry will offer you a glimpse of the difference.

Prof. Bartlett comments (though not cited from the purely academic source, sorry) that: 'It was clearly designed by an artist capable of detailed and close observation. For example, the Tapestry shows how Normans and English could be identified immediately by their haircuts. The English have shoulder-length hair and moustaches but no beards, while the Normans are clean-shaven and have their hair razor-cut dramatically high at the back' (Source).

On the other hand, the excessive employment of tattoos and their design are certainly much more annoying from a point of view of historicity. I'd recommend to check the negative comments of /u/Platypuskeeper, for example, in the following threads: [Added]: Is there a source describing the process of skin dying used by the Vikings? and In modern TV shows like "Vikings" and "The Last Kingdom", vikings often have a "tribal" appearance portrayed with big beards, face markings/tattoos, or eyeshadow. How accurate are these portrayals? Do we know what the vikings really looked like?.