The good stuff
As dark as the movie's content gets, it has a strong message about the idea that when people are willing to take great risks for the sake of justice, good can triumph over evil. And even when that evil is being perpetrated by the highest-ranking government officials, justice can be served. Also, you don't have to conform to society's standards to be a good and just person. Appearances are often deceiving; the most benign-seeming people can be capable of corruption and wickedness, while those whose appearances can be shocking may be virtuous and incorruptible.
Salander and Blomqvist are tenacious, courageous, loyal, brilliant, and honest. Women are portrayed in this movie as either competent, effective professionals or as dominated sexual victims. Government officials are shown as either corrupt, depraved, and willing to sacrifice anything to save face or as high-minded, justice-seeking individuals.
What to watch out for
Many intense, violent scenes. A hulking villain kills two police officers, breaking one's neck. A hospitalized man is shot in the head at point blank range; suicide by gun. A villain pushes a woman from a moving car; assassins spray machine gunfire into a cafe and are then killed by police. A stalk-and-chase scene ends with a gory capture. Also flashbacks to sequences from the earlier films in the trilogy that involve the initiation of a rape, a girl being shot in the head and dragged to a shallow grave, that same girl striking her assailant with an axe, and a man leaping from a car enveloped in flames. A brief view of a child pornography website is shown on a computer screen.
Though there's no overt sexual activity, major story points involve discussion of sexual violence and obsession. A young woman is partially nude, seen from behind.
Occasional swearing and obscenities: "d**n," "pissed off," "h**l," "s--t," "ba***rd," "Christ," "f--king."
Drinking, drugs, & smoking:
Moderate alcohol consumption in social settings. In two scenes, characters smoke cigarettes.