At Pedersen's first visit to the library, he is looking through a shelf of books. One of the books has the name Boris Yeltsin clearly made out in bold letters on the back, 25 years before his rise to power.
In (at least) two scenes Pedersen is walking up a steep hill in Larvik. In the harbor behind him you clearly see a funnel marked with the Colorline Logo. This company was established 20 years after the movie took place.
In the movie, Pedersen's wife leaves for the northern town of Mo i Rana, while in the novel, she goes to the town of Harstad. The director has explained that this change was made because she was a librarian, and that Norway's National Library has a branch in Mo i Rana. However, while the story is set in the 1970s, the National Library in Mo i Rana was not established until 1989.
When Pedersen is called in to the principal's office early in the movie, she is reading/taking notes in a book with a barcode on the front. Barcodes were used for the first time on merchandise in 1974, and these were not widely used in Norway at the time of the movie.