[Blomkvist:] "I assume that something happened to Harriet here on the island […] and the list of finite suspects consists of the finite number of people trapped here. A sort of locked room mystery on an island format?" (5.13)
This is, in fact, Henrik's theory. He's isolated from figuring out the truth because he won't entertain other possibilities. His mind is like a locked room. On some level he knows this, which is why he calls in Blomkvist.
[Blomkvist] could not for the life of him understand how he had allowed Vanger to talk him into this assignment. (8.118)
If Blomkvist wasn't feeling isolated as a result of being set up by Wennerström and being convicted of libel, fined, and sentenced to a prison term, Henrik probably couldn't have convinced him.
[…] [Martin] had taken the train home to Hedeby, arriving so late that he was stranded on the wrong side of the bridge accident and could not cross until late in the evening by boat. (8.145)
Martin is isolated on the other side of the bridge from Harriet when she goes missing, which means he's outside of Henrik's pool of suspects. It's funny because Martin has everything and nothing to do with her disappearance.
She would fold her arms and refuse to participate in any psychological tests. (9.38)
Salander contributes to her own isolation by refusing to be tested. At the same time, she maintains a certain power. Since she's never participated in the testing, the results are invalid and based only on the fact that she didn't cooperate.
[Palmgren] was not expected to regain consciousness. He was only sixty-four years old. [Salander] neither wept nor changed her expression. She stood up, left the hospital, and did not return. (9.54)
And thus begins a period of extreme isolation for Salander. She gets a new guardian, the sadistic Bjurman, and what happens between them isolates her further from people in general.
In the future, Bjurman would pay her bills, and she would be given an allowance each month. He told her he expected her to provide receipts for all of her expenses. (9.91)
Bjurman immediately sets out to re-isolate Salander by taking control of her accounts. By limiting her freedoms in this way, he can better control her. Or so he thinks….
The exact wording states that the guardian shall take over all the client's legal powers. In Sweden, approximately 4000 people are under guardianship. (12.5)
Salander's legal status isolates her from the rest of society. This quote shows that guardianship in Sweden (population nine million) is rare. Salander is a minority in this way.
[…] her only remaining action was to do what she had always done – take matters into her own hands and solve her problems on her own. (12.199)
Salander doesn't know Blomkvist yet when she takes on Bjurman, but what might his plan have been if she'd known him and confided in him? Remember this is before Bjurman rapes her in his apartment.
The message was written in all caps over five lines that covered his belly, from his nipples to just above his genitals: I AM A SADISTIC PIG, A PERVERT, AND A RAPIST. (14.93)
Salander is definitely trying to isolate Bjurman with these tattoos. No more swimming shirtless. The shame of it isolates him emotionally.
His time at Rullåker Prison had been unstressful and pleasant enough. The prison had been designed […] for hooligans and drunk drivers, not for hardened criminals. (15.2)
Being in prison and in isolation, free from all duties, seems almost like a relief for Blomkvist. Sometimes isolation can be positive and can allow for reflection and peace.
[Salander:] "He had that room for twenty-five years." (25.108)
Can't get much more isolated than Martin's dungeon on Hedeby Island. His wealth and power buy him secluded spaces where he can play out his crimes.
[Martin:] "While you [Blomkvist] sat and ate dinner with me, she was locked up in the cage down here. It was a pleasant evening, no?" (24.11).
This lets us know that during the time period when Bjurman was raping Salander, Martin had a victim in his basement. Blomkvist will probably never be able to forget Martin's words because he did have fun that night.
"I admit it. I just have no idea how it works. It's not only computers and telephone networks, but the motor in my bike, and TV sets and vacuum cleaners and chemical properties and formulae in astrophysics. I'm a nut case, I admit it: a freak" (27.96)
Salander's gifts make her feel isolated from society, because they are accompanied by an difficulty with socialization. These gifts are associated in the novel with Asperger's syndrome.
What did he need her for? Maybe she was just a way to pass the time while he waited for someone whose life was not a f***ing rat hole. (Epilogue.70)
We forget how vulnerable Salander is and how low her self-esteem is, when we see her in Zurich confidently stealing millions from Wennerström. A line like this helps remind us.