Tomas Alfredson has said that the production of " The Snowman " was too rushed. He came on board late and reckons that up to 15% of the screenplay was never filmed. In addition, the location filming in Norway was shortened so that the production could move to London, which compromised the story.
The Schrøder Restaurant where Harry Hole is regular guest in Jo Nesbo's book actually exists in Oslo and part of the filming took place in there. Also, according to the book, Harry's home is at Sofies gate 5, which is a few minutes walk from Schrøder.
The Snowman (2017) and Downsizing (2017) were the first two international features shot in Norway to receive funding from the new state incentive program to attract foreign film and TV productions. The two features spent together $24 million in Norway during their Norwegian location shoots. 
In the eponymous book the police discuss several Swedish serial killers, among them Thomas Quick (a.k.a. Sture Bergwall). However, Quick/Bergwall was eventually acquitted of all the alleged murders. Brother Sten-Owe Bergwall and lawyer Pelle Svensson wrote books criticizing the Swedish authorities' handling of the cases.
Although mostly shot in Norway, great care was taken to remove any Norwegian language from the movie. No Norwegian is spoken and anything normally written in Norwegian is changed. This includes newspaper headlines and destinations on public transportation. Norwegian police cars normally have "politi" written on them (meaning "police") but this was simply removed.
Apparently, Fassbender bought drinks for the whole crew after a long day of shooting. The next day, rigging electrician Karl Andre Bru walked up to the famous actor and said jokingly: "thanks for the hangover, man!". Rumor has it Fassbender cracked up and was unable to keep a straight face for the rest of the day.
Leading up to the release of the movie, the newspaper Verdens Gang released a series of mock articles in collaboration with Universal. This was meant to show how the newspaper would normally cover a case like the one depicted in the movie. Included were articles about the murder weapon, Harry Hole himself as well as grisly details from the antagonist's murder spree.
Rebecca Ferguson shot The Snowman before the press junket for Despite The Falling Snow. She references having just shot the film in one of her interviews where she is still growing out the fringe that she has in The Snowman.
The trivia items below may give away important plot points.
In the final scene, Harry volunteers to investigate the murder of a woman who was found with 24 stab wounds in her mouth from an unidentified weapon. This alludes to the events of the novel "The Leopard", published after "The Snowman".
The movie's plot strongly deviates from the novel's, taking huge liberties that fell under strong criticism, notably killing off the character of Katrine Bratt (played by Rebecca Ferguson) when she has actually appeared in three subsequent entries of the Harry Hole book series, so far ("The Leopard", "Police" and "Thirst").