When Lisbeth Salander goes through financial verifications of Vanger Group 1949-1965, an account statement from Skandinaviska Enskilda Banken appears. Skandinaviska Enskilda Banken, however, was established in 1971.
When Mikael visits Henrik Vanger in the hospital, he is supposed to be recovering from a cardiac bypass. There is no evidence of a chest incision which would be visible with his partially open pajamas and robe.
When Lisbeth and Mikael have breakfast in the cabin, Lisbeth is putting ketchup on her breakfast. In the view of her from the front, the ketchup reaches all the way to the bottom of the plastic bottle. In the next shot, facing Mikael, the bottom of the bottle has almost no ketchup at all.
There's a sentence at the bottom of the e-mail sent by Lisbeth: "Read it and weep, Kalle Blomqvist..."
The scene changes, Mikael takes a better look and reads the sentence which is now, "Read it and weep, Kalle Blomkvist..."
When Mikael discovers the names and numbers in the back of Harriet's diary, Harriet's voiceover reads them (and they are visibly written) as "Magda, Sara, BJ, LJ, Mari". Later in the film, "LJ" is changed to "LI" with no explanation.
The postage stamp at the beginning of the movie shows it is from Hong Kong. The Chinese characters on it are written in simplified Chinese script, rather than the traditional Chinese script used in Hong Kong (and Taiwan).
When Martin's Land Rover rolls, one shot shows it artistically ending up on its side just shy of a tree. However, the previous angle and the final view show the Land Rover plainly resting flat on its roof instead.
When Blomkvist is injured at his left temple, one can see that the wound is created on some fixation tape like Op-Site. There is an easy detectable wrinkling in the fixation tape that doesn't match the skin.
In Australia, Mikael drives to Harriet's place in a pickup truck. Australia mandates left hand drive, with the driver on the right. When he puts his bag into the truck's right-hand seat, the steering wheel is clearly absent. In subsequent interior and exterior shots he is sitting behind the wheel and also exiting on the right, so possibly those shots were flopped (although the license plate and car brand aren't mirrored).
The video camera that Lisbeth used to film Bjurman raping her was one using a DV tape; however, after coming home, Lisbeth turned on the camera and immediately watched the rape scene. On that model, she would have to rewind the tape first.