Diagnosed by the Audience: Due to her risky behavior and Mood-Swinger tendencies, Alaska having Bipolar Disorder or Borderline Personality Disorder is somewhat of a popular fan speculation. Of course, it's equally possible—likely, even—that these symptoms were simply brought about by deep emotional trauma.
Do Not Do This Cool Thing: Both supporters and detractors of the book commonly see Green as glamorizing or even outright endorsing Miles and his friends' reckless lifestyle, including copious underage drinking and smoking, playing highly destructive practical jokes, and a code of silence on the above matters that would make the Mafia proud. This is despite the fact that a chain of Disaster Dominoes involving all of the above literally kills one of them. Green himself was disappointed that many readers got the exact opposite message than he was intending, and his third novel Paper Towns, in many ways a Lighter and Softer take on Alaska, makes the themes a lot more explicit.
Ending Fatigue: A number of fans find the fact that over a third of the book is Dénouement to be excessive.
Fandom-Specific Plot: There are a number of fics that run with the notion that Alaska faked her death, often as her most ambitious prank yet, as Miles initially speculated. She is Just That Good, after all. Another common topic is depicting Alaska's death from her perspective, including her mysterious last words. The latter element in turn comes in two varieties: either she's thinking of Miles, or it's something amusingly anticlimactic, e.g. "Shit."
Fanon: Green intended for the circumstances of Alaska's death to be, well, a mystery, with various details pointing to several possibilities (that it was a suicide, or that it was an accident). However, you will find that fans tend to incline more towards the notion of Alaska's death being in some form suicidal. This is because of her well-established mental illness and sadness; people have no difficulty believing that her internal pain that night would've been enough to trigger suicidal tendencies.
Follow the Leader: John Green's subsequent works tend to have more than a passing resemblance to the characters and plot already featured in LfA, particularly Paper Towns (though that book is an intentional Deconstruction of LfA).
Misaimed Fandom: Alaska's rebellious behavior wasn't cool; it was a massive red flag that the others ignored. She was only so hedonistic because it temporarily distracted her from her trauma and she never learned any better coping mechanisms. And had any of the others confronted Alaska over her bad habits instead of going along with them, she might have survived.
Narm: The sheer amount of Contrived Coincidence that sets up the book's big disaster can be a bit hard to believe. Among several other steps, it involves not one but two missed anniversaries just happening to fall on the same day, as well as a phone call by exactly the wrong person to exactly the wrong other person about exactly the wrong subject at the absolute worst possible time.
Anyone you know could die in a senseless accident and you will never know if you could've prevented it.
Think of anyone you care about. Now think, do you really care about them, or just your idea of them?
Recycled Premise: Here's the story of a loner of a boy who had an awkward friendship with a hyperactive girl with a quirky imagination, who happens to live next door to him and taught him to socialize and interact with others. Unfortunately, shortly after changing his life for the better, the girl dies a sudden and untimely death, leaving the boy to cope with the aftermath of her demise, before finally accepting that she's gone for real. Sounds familiar?
Spiritual Successor: To The Virgin Suicides a decade earlier. Both deconstruct the Manic Pixie Dream Girl trope, talk at great lengths about the dangers of men putting women on pedestals, and have a major plot arc about characters searching for answers following a tragedy and finding none. Green commented on his blog that Virgin Suicides was one of his favorite books as a teenager and though he didn't intentionally draw from it he wouldn't be surprised if he was subconsciously influenced.
Strangled by the Red String: One of the few intentional (and well-done) examples with Miles and Lara. They have approximately less than zero chemistry and hook up without any sexual tension or build-up... but this makes sense. There is no substance to their relationship. Lara appears to take no interest in forming a deep connection with him, while Miles is already in love with Alaska.
It's possible Alaska only decided to try hooking them up because she knew Miles had feelings for her, but she was already in love with Jake and didn't want to destroy Miles in the process. So she picked the first girl who had a crush on him.
Each character gets a turn at this when they play 'Best Day, Worst Day'. Lara had to leave her childhood behind when she moved from Romania to America, Pudge was humiliated in seventh grade and vowed to Stopped Caring (until he came to Culver Creek), The Colonel's dad walked out on him after being an abusive partner to his mother, Takumi watched his grandmother burn on a funeral pyre and Alaska watched her mother die right in front of her, then her father blamed it on her. Ouch.
Alaska's death, full stop.
Miles' epiphany at the very end, particularly the following line:
But the not-knowing would not keep me from caring, and I would always love Alaska Young, my crooked neighbor, with all my crooked heart.
Whether or not it improves upon the book. This seems to be a case of mild Critical Dissonance, as most professional reviewers thought it better fleshed out the novel's story by adopting a broader and more mature perspective beyond Pudge's biased point of view and taking time to explore the inner lives of secondary characters like the Eagle. Diehard fans of the book, while generally accepting it as a worthy adaptation, argued that it demystified Alaska a little too much and that Pudge's flawed and limited perspective was one of the story's strengths.
The matter of the series confirming that Alaska does indeed return Miles' feelings. While supporters of the pairing obviously enjoyed this, and others simply felt it was confirming something that was already heavily implied in the book, still others criticized it due to getting rid of one of the story's big mysteries and one of the unknowns Miles grapples with after her death.
Ensemble Dark Horse: Believe it or not, Jake, who goes from a bland romantic obstacle in the book to an unexpectedly endearing and nuanced character thanks to an adaptation-exclusive subplot in Episode 3. Many fans found themselves agreeing with Alaska's assertion that he's too good for her, and happy that the show provides him with an implied Second Love in the form of Fiona.
Heartwarming Moments: Though it undeniably sheds the tragic ambiguity present in the book (see Broken Base), seeing Miles and Alaska finally act upon their mutual feelings is incredibly cathartic after five episodes of buildup.
Moral Event Horizon: Longwell and Kevin in Episode 5 when they destroy Alaska's beloved book collection as payback for turning in Marya and Paul. Even the other Culver Creek students, to whom "Don't rat" is the first and only commandment, think that's too much, and the tour de force of a prank that her friends pull in response reconciles them after they had fractured in the previous episode.
Tear Jerker: The lingering look that Miles and Alaska share as he holds the campus gate open for her to drive away into the night. It's the last time the two of them ever see each other. It also gives him a more direct role in enabling her death than the book.
