In the discussion at St Stefans after Zalachenko has been killed, Peter Teleborian is told that it is vital that Lisbeth is convicted of shooting Zalachenko. Yet she didn't shoot him at all - neither where they were both found and taken to hospital and certainly not at the hospital; she attacked him with an axe and took his gun, but did not shoot him. The statement should have been that it is vital that Lisbeth is re-committed.
When Lisbeth wakes up at the hospital the doctor is wearing a shirt with the logotype of "Stockholms Landsting" i.e. the health care provider of Stockholm, although she is supposed to be located at Sahlgrenska University Hospital in Gothenburg.
When Lisbeth is in the operating room, the bullet is removed from the left side of her brain, as depicted by the frontal view X-ray that is hung on the X-ray view box, which shows the bullet on the left side of her head (viewer's right side). After her surgery, the operative side of Lisbeth's head (as demonstrated by the dressing and her shaved head) is the right side.
When Erika Berger comes into the Millennium offices and turns on her computer before finding another email threat, it is clear that her computer is already on before she reaches over to press the button because the Apple light is already on.
In the flashback footage from The Girl Who Played with Fire when burning Zalachenko falls out of the car, he falls next to the container and the spilled "gasoline" that splattered when Salander threw it on him and dropped the container, but it doesn't ignite, proving it isn't gasoline.
When Niedermann kills the policewoman (seen in long shot), her arms are hanging loose at her sides. When it cuts to close-up, her hand is grasping his arm. Not only has no time passed between the long-shot and the close-up, but it would be impossible for her to have reached up and grabbed his arm after her neck is broken.