The crew were not worried about whether the ropes would hold the float together, as it is portrayed in the film. As we can see in the Kon-Tiki (1950) documentary, the balsa wood was much softer than the rope, and it was actually the rope that ate through the wood. The result was that the rope eventually was protected by the space that had been created around it.
When they encounter the whale shark, it releases air when it dives beneath the raft. Later on it "blows" in the distance. Whale sharks, like all fish, are not air breathers, and thus do not release air like a mammalian whale would do.
It is not true that every 13th wave is larger than the others, as claimed in the film. In fact, there exists no pattern in wave sizes. In the original Kon-Tiki (1950) documentary, it was shown that the crew simply waited for a wave big enough to carry them over the reef.
Herman Watzinger is portrayed differently to how he was in reality --- he was tall and a champion swimmer, and never worried about the ropes breaking. Also, he did not harpoon a whale shark, it was Erik Hesselberg, and the crew cheered him on.
When Thor translates the Polynesian chief's words from French to English for Liv, he actually translates phrases before the chief has said them.
When the radio operator makes first contact with an American station before the parrot severs the antenna wire, the Morse Code he uses is nonsense.
The scenes on Fatu Hiva were shot in Thailand with Thai extras who do not resemble Polynesians. Also, the "natives" are holding compound spears and weaving rattan baskets, of which neither the technique nor the plant material are native to the Marquesas Islands.
One of the characters uses the counting method introduced in 1951 (1st July) when reporting Kon-Tiki's position. He uses the word 'femtifem' (English: fifty-five). In 1947, when this film is set, he would have used 'fem-og-femti' (English: five-and-fifty).
As this old-fashioned counting method is used by many (younger) people today, the new counting format is still debated in Norway and the film-makers may be expected to be aware of this.
At one point in the movie we see the cover of a Norwegian passport, it is printed with "NORGE NOREG" and also includes additional text. This duo-language Norwegian passport was not introduced before in the 1970's. In 1947, the only text on the cover was "PASS"and"NORGE."
It is obvious that Kon Tiki was not filmed anywhere near the west coast of South America. The cold Humboldt (or Peru) Current comes from near the Antarctic, flowing north along Chile and Peru. It then swings westward out as far as 1,000km into the Pacific. The weather off Peru is often total overcast and cold enough for sailors to wear a sweater. The film only shows lots of sun and blue skies.
When Bengt tells Thor about terrible water streams near Galapagos islands, he shows him a book with an illustration. But the book he shows has nothing to do with Galapagos --- it is a drawing by Harry Clarke made for a 1919 reprint of Edgar Allan Poe's short story "A Descent into the Maelström," and shows an exaggerated portrayal of the Moskstraumen whirlpool near Lofoten archipelago, Norway.