The story takes place in about 2005-06. Mikael and Lisbeth are using Macbook Pros with older versions of OS X, which correspond with the time. However, the Macbook Pros with black separated keys were not introduced until 2008.
Henrik stands with Mikael outside in a snow storm showing him where each family member lives and how they're each related. He points to a nice and up-kept house within walking distance of Henrik's house (the main house) and says Isabella lives there, but later Isabella's son, Martin, claims Isabella was "excommunicated to the old house on the other side of the island."
When Blomkvist is reviewing Inspector Morrell's notes from the accident, he highlights what he considers to be interesting facts. One of them is about Inspector Morrell interviewing the family, however, "interview" is misspelled "interveiws".
When Lisbeth is checking Mikael's email in the beginning of the movie, the incoming emails are all dated "2/1/06" (thus indicating either January or February depending on date setting), whereas the next scene takes place either on Christmas Eve or shortly after.
When Cecilia is looking at a family tree diagram on a wall in Mikael's cabin, the camera focuses on two paper sheets containing photos, Post-It notes and name labels about Cecilia and Harriet. When it zooms out, the photos, sticky notes and labels are arranged in a very different way.
When Lisbeth searches Hans-Erik Wennerström on Google, the search results list a Wikipedia article first that lists Hans-Erik Wennerström's birthday as "May 29, 1952." When Lisbeth clicks through to Wennerström's Wikipedia page, it lists his birthday as "12 June, 1951."
Stockholm has two types of subway trains in use, the old original trains and the new trains. In one clip Lisbeth is sitting in a train with the old interior, i.e. an old train. The next clip shows the train from outside (meeting another train at Slussen), but both trains are new, not old.
Blomkvist's MacBook Pro magically downgraded itself from Mac OS X Lion to Mac OS X Tiger during the movie. Even if he did want to downgrade the OS himself, that would be entirely impossible due to the fact that Tiger cannot run on the hardware present in the Macbook Pro displayed.
During the chase scene; when the camera is pointing back towards Lisbeth, her face is lit by the glow of the motorcycle's instrument cluster (speedometer & odometer). But when the camera switches to her point of view; the dials are dark and not lit up.
Toward the end of the movie, Salander travels to Switzerland using a fake Norwegian identity. She is shown using a Norwegian passport at immigration in Zurich airport. However - Sweden, Switzerland and Norway are all part of the Schengen Area. Salander would not be subject to passport control on the Swiss border if her inbound flight originated in Sweden or Norway.
On Wennerström's Wikipedia entry, all the "blue links" are external links (denoted by an icon at the end of each link). That amount of external links in the body of an article in Wikipedia would be considered spamming and is forbidden. External links in Wikipedia (when deemed reliable and pertinent enough) normally go to a section at the very end of the article.
Frode tells Mikael (as if he would not know it) that it has been coldest winter in 20 years. Sea is not frozen, there is very little snow, and you can see wet snow coming down from fully clouded sky: Temperature is obviously close to zero Celsius. Besides, this happens right before or after New Year, when coldest time of year is just beginning at this part of world.
The action in the movie takes place in Sweden, but almost all of dialogue is in English. The movie makers have gone to great pain throughout to translate documents, notes, emails, newspaper reports etc. into English. However, on the wall where Mikael's pins his research material, some of the newspapers are clearly in Swedish. At one point, he picks up a news clip with the headline "Gottfried Vanger påtraffad drunknad" (Gottfried Vanger found drowned) which is inconsistent with the rest of the movie.
When Salander is searching crime records she is entering SQL queries, but the result does not match her query. The query specified last names starting with the letter "L" but the result included names that did not start with "L".
Mr. Vanger, The grand father of Harriet, tells to Blomkvist(Daniel Craig) that, Harriet used to gift him framed-flowers every year on his birthday. And he says, the flower-frames on the left side of the wall are by her, and those on the right side of the wall are from her killer. But there are 18 birthday-gifts by Harriet on left side. It means she gifted them on 18 birthdays of Grandfather. But she went missing when she was 16 years old. This is not possible even if Harriet started to gift framed-flowers to her grandfather ever since she was 1 year old. (Even then only 16 framed-flowers should be on the left wall).