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The most common complaint during its first season is the frustration people had about characters not sharing vital information with each other. This is never explained within or outside the show.
As referenced in the title of the episode, what did the Candidates of Season 6 "die for"? This was never explained.
It has not been explained, and probably never will be explained, why, in Season 2, the Others did not capture Jack, Sawyer, Kate and Locke when they had them surrounded and disarmed in "The Hunting Party" - only to later offer Michael the following deal: "we will give you Walt and a boat if you bring us Jack, Sawyer, Kate and... Hurley." (They only needed Hurley as a messenger.) This is particularly jarring if you consider that, in The Hunting Party, these facts hold:
Ben had not been captured yet, and so they didn't need Michael to rescue him yet.
Ben was already aware that he had a tumor and needed Jack.
However, Ben didn't know yet who else he needed to kidnap in order to manipulate Jack into doing the surgery in case the brainwashing didn't work. Ethan was probably too obsessed with Claire to pick up on the relationships that had only been set in motion, what, a week? That triangle was ripe pickings. And it worked.
Blame it on "writing it up as you go along". "Henry Gale" was introduced 3 episodes later, and the writers have stated he was just a guest character, but Michael Emerson impressed them so much that the role was expanded. Ben's story wasn't fully developed, which makes this become Fridge Logic once you know the whole thing.
The insane trial of Kate in season four. Somehow, the numerous charges against Kate, including murder, assault, and theft, are all rendered moot because her mother refused to testify against her.
Not to mention that a lot of these were in the wrong jurisdiction.
The flash-sideways in general seemed lame, what with taking up half of each episode while appearing to have zero relevance to the main plots or characters. But "What Kate Does" takes the cake by giving everyone a Idiot Ball. Kate doesn't even bother keeping a low profile; she goes right up to a mechanic saying "I'M A FUGITIVE MURDERER!" After being held hostage by Kate when she hijacked her cab, Claire takes all of a second of thought before jumping back into the cab and traveling around with Kate as she goes to see Aaron's potential adoptive mother. And then she hands over her credit card to Kate so she can have money on the run... What?
Ilana's death. Not only did they leave another character's backstory unexplained with just a handful of episodes left, not only did they go out of their way to ignore her all season despite the actress being made a regular and her being the leader of one of the two main factions, but it also happened in the most idiotic way possible. Ilana was training for the mission all her life, but didn't know that the candidates can't kill themselves (which presumably included mishandling dynamite)? She didn't know how to handle dynamite? Her death serves no purpose: the audience was already aware that dynamite was dangerous from Arzt, and the dynamite could have been gotten rid of another way.
"Across the Sea." Wasting an entire hour on a supposed backstory for Jacob and the Man in Black that doesn't answer much besides the identities of Adam and Eve, all while the writing gets more and more awkward to avoid having anyone refer to the Man in Black by his name (under the circumstances, there should have been a way to do it that wasn't awkward). Oh, and just after Lindelof and Cuse made such a big deal about killing off Jin and Sun to cement the Man in Black as a Complete Monster, the entire episode makes him more sympathetic than Jacob!
To some, he came across as more of a devious spoiled brat.
Sayid's "soulmate" is revealed to be... Shannon, the woman he had a brief month-long relationship (in the loosest sense of the word) with on the island, as opposed to Nadia, the woman he searched for years to find and lived happily with until she was killed in a hit-and-run accident. Uh...?
The subtext of the show is that all the characters are obsessing over something, whether its mysterious lotto numbers, long lost loves, destiny, fixing everything, etc, and this obsession is the root of their suffering. This is pretty elementary Buddhism, which the show has been trucking in since the season 2 premiere. In the afterlife, he subconsciously recognizes how he caused himself to suffer, and marries her off to his brother.
Jack's conflict and reconciliation with his son David is revealed to be nothing more than a figment of his imagination, rendering the entire plot thread (played out of the course of the whole season) completely pointless. While it is explained that Jack has to resolve his own issues before moving on, it does nothing to make the conversations any more than filler.
The Man In Black's ultimate plan is to get someone to remove a literal "cork" in the island's core (which will supposedly submerge the island), get on a boat and escape... and then what? Not only is his idea half-baked at best (he runs away while leaving three people there who could fix the situation he just caused), but everyone else acts like him getting off the island will mean the death of mankind - even though by the time he's killed, he's just a mortal man. He has no allies outside the island, let alone that he no longer has his superhuman strength or his "smoke" powers - his plan was illogical and not feasible.
His plan seems to have been only to leave the island and live as a mortal, even with no allies or money or wtf. Only Jacob tells everyone that he's evil and threatens mankind, but Jacob is either completely wrong about it, or (most probably) simply lying to make people do what he wants, as Ben did during the whole show.