The Millennium Trilogy as a series contains YMMV examples of:
Angst? What Angst?: Played with in Lisbeth's case. On the one hand, she has been deeply marked by her terrible childhood experiences, but on the other hand, this has made her pretty much impervious to any later trauma. Her reaction to being brutally raped and tortured for an entire night is to very calmly get revenge, and then move on without any sign of being hurt by it. Her reaction to being shot in the head and buried alive is likewise to get revenge, and then function pretty much exactly as she has always done.
Between the fans of Noomi Rapace as Lisbeth and those of Rooney Mara's version. Or, if you prefer, English vs. Swedish versions. Making it more interesting is that the Swedish Dragon Tattoo film is more faithful to the tone of the novel, while the American one is more faithful to the plot, so everyone gets to decide which is more important to them.
In regards to the books: The Larsson books or Post-Larsson books. Either you're okay with the series continuing and trying to fulfill Larrson's idea of ten books within the series or you find it a complete middle finger from Larsson's family decided to continue the series and disregard the fact his partner, Eva Gabrielsson should be a part of Larsson's estate (as she owns the last of the planned manuscripts Larsson had written before his death) due to the two never being married, as both Larsson and Gabrielsson did intentionally to avoid being tracked due to their anti-fascist work.
And regardless of your thoughts on whether or not you were okay with the series continuing, The Girl in the Spider's Web was met with mixed reviews. Some enjoyed the plot and characters and were warmly receptive of it as a continuation of the series, while others found that the writing and plot failed to live up to Larsson's and flanderized both Lisbeth and Blomkvist.
Complete Monster: Besides the Vangers, the other two books have Alexander "Zala" Zalachenko, a Russian agent who took refuge in Sweden. Because of his high importance to the government, Zalachenko was allowed to do anything he wanted. His favorite activity was abusing his wife. He would often torture or beat her in front of their daughter. The last time, he beat her so bad he left her with severe brain damage, which resulted in his daughter, who we find out is Lisbeth, burning Zala alive in retribution. Surviving with hideous wounds, Zala became the leader of a powerful human trafficking ring where girls were forced into prostitution (he abandoned a more lucrative career as a drug dealer for this profession; it is thus strongly implied he is in this job out of spite. Having many, many women sold into sex slavery or killed when their value diminished, Zala also had multiple murders committed by his nightmarishly powerful son, and when he found out his daughter's location, he spared no expense to murder anyone in his path to torture her to death himself.
Designated Hero: Lisbeth Salander may rarely be in the wrong, and may be up against more depraved people than herself, but she's still a deeply scary human being.
Ending Fatigue: A fairly common complaint about the first installment. After Harriet's murder is wrapped up, a lot of time is spent dealing with Blomkvist's and Salander's revenge against Wennerström.
Fan-Preferred Couple: More than one fan expressed disappointment that Larsson asserts Lisbeth's feelings for Mikael are gone after the first novel, age gap and personality divide be damned, and find their respective Official Couple partners forgettable or undercooked. As Spider's Web makes these partners disappear and ends with Lisbeth going to Mikael's apartment (to renew their friendship), shippers tend to view it with romantic undertones.
Jerkass Woobie: Despite all her attitude problems, there are times throughout the books when so much gets piled on her that you just want to give Lisbeth a big hug. Preferably when she's not holding a Taser.
Misaimed Fandom: Many feminists like to look at Lisbeth as a role model because she goes out of her way to beat up misogynistic pigs.... ignoring the fact that it is made explicitly clear that not only is Lisbeth a violent person who repeatedly goes above the law to achieve her own ends, she's not portrayed as a feminist in the books, as she is supposed to be a stand in for those who are subjected to violence and being taken advantage of. She also doesn't fit into any kind of social classification, including feminism, which was another point of her character.
Some Anvils Need to Be Dropped: The three books have obvious messages against violence/mistreatment towards women, government and business corruption, and abuse of power in general.
Strawman Has a Point: Teleborian may be a sadistic Smug Snake and a prolific pedophile, but he is correct- promiscuous sexual behavior is indeed a marker of sociopathy. Its not, in and of itself, enough for a diagnosis, but Lisbeth setting her dad on fire (even if he deserved it) didn't do her any favors as far as that goes, nor did her history of truancy and alcohol abuse or her evident (if justified) paranoia. He is ignorant of her torture of her (sexually abusive) social carer and her career as a world class cyber criminal, which is just as well for her because all in all he could make a pretty convincing case. She might not be a true sociopath, but she certainly displays many sociopathic traits.
Values Dissonance: From the Swedish perspective, a 16-year old is not really a child when it comes to having sex.
The Girl With The Dragon Tattoo contains YMMV examples of:
Award Snub: Rooney Mara losing the Oscar for Best Actress is seen as this. Trent Reznor and Atticus Ross' score for the film wasn't even nominated at the Oscars.
Martin Vanger is a polite, charming CEO who uses his position in society to cover up the fact that he is a Serial Killer and rapist of women, kidnapping them and spending days raping and torturing them before ending their lives. Martin has been committing his atrocities for decades, and his victim count handily reaches into the hundreds. Even worse is the reveal that Martin was raised to be a killer by his equally repulsive father, Gottfried, and though potentially tragic, it is made explicitly clear that Martin just enjoys raping and killing, made all the more obvious by turning his own sister into his personal sex and torture slave after his father is out of the picture. Martin tries to subject Mikael Blomkvist to the same torments of his previous victims in the end, and simply excuses his crimes by proclaiming it is his hobby and he is living a "complete life".
In the 2011 film, Gottfried Vanger is a more onscreen menace than his novel counterpart. A fanatical Nazi with an obsession for mimicking and mocking the Bible, Gottfried murdered more than 6 women in horrific ways resembling punishments from the Book of Leviticus, always subjecting them to brutal rape and torture beforehand. Be it by bashing their skulls in or raping them to death with farming tools, Gottfried perpetrated his acts with zeal, and took his own personal sadism to such a level that he sexually abused his own son and daughter, helping the former—Martin—realize his love for killing while turning the latter—Harriet—into his toy to be tortured until he finally tired of this and attempted to murder her.
Moral Event Horizon: Bjurman - who is Lisbeth's legal guardian and caretaker - crosses this line when he forces her to perform oral sex in exchange for the money she needs to replace her computer. And then longjumps even farther over it when he violently sodomizes, rapes and tortures her.
Nausea Fuel: Blomkvist's adopted pet cat being left on his doorstep with its head missing and every limb snapped clean off.
Slow-Paced Beginning: The book gets off to a slow start, with a lot of infodumping about Blomkvist's legal troubles in a story that's supposed to be mystery. This thread doesn't get picked back up until the very end, causing Ending Fatigue. Meanwhile, the book's whole first half cuts between Blomkvist and Salander's stories seemingly at random, making it quite a relief when they finally join forces. It's likely that Larsson would have done some editing to make it flow better if he'd lived.
Spiritual Licensee: Not the entire film, but the opening credits to the 2011 American version are extremely reminiscent of the title sequence to a James Bond film, complete with surreal, sexual imagery and a dark, thrilling lyrical song. Bonus points since the American version stars Daniel Craig.
Squick: Lots of it. Most of all, the biblical serial murders and Harriet's history of being raped repeatedly by her father and brother - once by her brother immediately after she'd murdered their father (while "his body was still floating in the water), to boot!. Lisbeth has a bit as well, when she gets revenge on Bjurman.
Moral Event Horizon: Zalachenko crossed it when he beat Lisbeth's mother so badly that she suffered a crippling cerebral hemorrhage.
The Girl Who Kicked The Hornet's Nest contains YMMV examples of:
Harsher in Hindsight: At the beginning of the novel, Blomkvist says that he is going to talk with Dag and Mia's families about the publication of Dag's books, to get their opinion. In Real Life Larsson's family was much less considerate about the manuscripts, publishing them without his partner's consent.
Moral Event Horizon: Even though he's trying to screw up Lisbeth's life, Fredrik Clinton crosses this when he arranges for Mikael to be murdered and framed for dealing drugs in an effort to destroy his credibility. Wadensjö even calls him on it, saying that Clinton will end up destroying The Section because of his actions.
Seasonal Rot: Generally considered the weakest in the series, with the gripping action of the first two novels put aside and more ponderous legal drama taking the stage.
Strangled by the Red String: Mikael and Monica each admit (separately) to Erika that "I think I'm in love with her/him". But despite this declaration, Mikael isn't sure if it's serious. Indeed, despite an obviously strong mutual attraction, there's really nothing to suggest this will be anything more substantial than the numerous flings he's gotten into throughout the trilogy.