Throughout the series, Nagato seems completely robotic, with no emotions whatsoever other than in their battle against the computer club in a strategy game, and even then, Kyon has to point it out for it to be easily noticed. Then Disappearance happened. Suddenly, incredibly minor things she's done through the whole series make sense and imply emotion.
The movie version of Disappearance gives a subtle hint that Kyon was never alone in the hospital before it's revealed Haruhi was there the entire time. If you look closely, next to his bed there are a pair of girl's shoes. Her coat is also clearly seen hanging in the foreground on several shots. The weird thing is that her shoes are on the opposite side of the bed than the one she's sleeping on. What was she doing when no one else was around?
During Disappearance, Yuki remakes the world to a more ordinary one. One possible reason she went to these lengths is because of what she experienced during Endless Eight (spending hundreds of years trapped in a time loop Haruhi caused). So how could the anime possibly replicate something like that? OH! Make the anime version feel like it's going on foreverexactly like it is for Yuki!
Why does Haruhi never turn down a boy who asked her for a date, even if she subsequently dumped them five minutes later? At first, it's put down to one of her many strange quirks. But she's a Reality Warper who causes anything in the universe to mold itself to her desires. Thus, the only boys who ever ask her out are the ones she already wants to go out with.
The final chronological episode of season one. At first it just seemed cool for the fact that the makers actually had the balls to make an episode of a show which was at least 40% someone sitting and reading quietly. But the whole point was a) to show what a non-weird day in a television character's life is like, b) to show how bored the SOS Brigade would be without Kyon, including Kyon and the viewer. Observe - with nobody to philisophise with, Itsuki ends up talking to himself about the weather and his tea. Without Kyon to act as a Morality Chain, Haruhi ends up doing her worst to Mikuru, and doesn't have anyone to bounce/steal ideas off. Without Haruhi going totally nuts, Yuki has nothing to do but read, and hence no reason to talk to anybody. Without anybody to be pissed off at, Kyon is thinking about the weather. Without Kyon snarking, listening and accidentally suggesting ideas, the viewer gets really, really bored. Suddenly a hilariously boring episode becomes brilliant.
Yuki's abilities to travel through time (sorta), leads to the question of why on Earth Kyon couldn't just ask Yuki to find out the future about Haruhi and what happens, etc. Then post-Disappearance, Yuki makes the decision to block out her ability to time-travel beyond the incident. Brilliant, Tanigawa.
In the English version, Stephanie She's portrayal of Mikuru can seem like going overboard with the cute, shy girl thing. But if you watch the Japanese version, you'll realize Mikuru's voice is supposed to be annoyingly cute as part of her being a parody of Moe characters in anime. A lot of characters are intentionally annoying; skilled authors will hide this fact well. The hope is that you'll associate them with someone you don't like and thus make the world of the show more alive for you. I don't think anyone will argue there's a shortage of those people. Upon realization of this fact, scrappy characters gain a little respect. They're there for a reason, and taking them away will destroy a large part of the show. It's still on the creator not to overdo it, however.
When the first seat-change happened in the first novel and Haruhi ended up behind Kyon again "coincidentally", the obvious assumption is that it was because of Haruhi warping reality slightly so she could be near him. But Asakura, as class president, had been the one to change the seats. Wouldn't she want Kyon to be near Haruhi to provoke a response from her? Related: There are more seat-changes after the first, after Asakura is gone, and Kyon and Haruhi still end up together. That could be her powers at work, or it could be the teachers rigging the lottery, since they are well aware Kyon is the only one with some semblance of control over her.
Why Yuki was elected to be the ambassador to the Sky Canopy Domain:
Kyon stopped the IDSE from killing Yuki. There was a loophole though, which the Genre Savvy/super intelligent IDSE saw.
Alternatively: Nagato has spent close to six hundred subjective years observing humans with most of that time in a state of And I Must Scream. She has dealt with insanity that the IDSE could not even fathom, wouldn't that, then make her the most ideal candidate for dealing with the Sky Canopy Domain? Rather than thinking of the IDSE as a child angry that something was taken out of its control it would be more likely to think of it as a computer using the most suitable resource available.
Every time that Kyon copies a graphic designed by Haruhi, a data-vore appears. Perhaps it's not so much a his/hers divinity, but a theirs.
Yuki and Ryoko's actions in Disappearance didn't make as much sense as they should have. Yuki was bored and upset and angry and tore apart reality out of vengeance. But why did she give Kyon the keys back to his reality? And why did Ryoko still stab Kyon? But if you look at them as complex programs, rather than humans, it makes sense. Yuki is hard-coded to be a servant and an observer—but she is able to change who she serves and observes. It's also probably possible that they can re-hard-code themselves (or that the radical faction gave their interfaces this ability)—Ryoko remembers the alternate timeline. Given her determination to kill Kyon during the first murder attempt combined with her seeming lack of emotion, it's perfectly possible that she re-wrote herself to kill Kyon at all costs (though the reason why might be irrelevant to her coding). Therefore, given her own existence and Kyon's presence, she's gonna go for it. This also explains why she didn't try to murder him at school 'later that day'—she had already done so, so there was no longer a need to kill him again.
At the Cultural Festival, when Nagato is reading people's fortunes, you just naturally assume she's able to get so incredibly specific because, being a computerized alien, she's a beast at logic. Although, if you recall, earlier on in the timeline, when Kyon needed to get back to his present time from three years ago (for the second time), Nagato synched her memories up with those of herself from the present day, which was beyond the Cultural Festival chronologically. That would mean she would have memories of the Cultural Festival also, even before it actually happened.
So on the Tanabata that started everything, Haruhi drew a large patch of symbols on the school blacktop because she was really,really,bored. These symbols, along with the awakening of Haruhi's powers (both happening at around the same time), drew the attention of various aliens, time travelers, espers and about a million other things that we don't know about. Haruhi drew those symbols with the goal of alerting all the strange and interesting things in the universe that "I am here", much like how a person stranded on a deserted island would try to get the attention of passing ships and planes. So in other words, on that faithful Tanabata where the entire plot of the series was planted, Haruhi was sending out into space a distress signal. In other words, an SOS.
This one is probably more like Obvious Brilliance to the Japanese viewers, but it kinda gets Lost in Translation: in Disappearance, it's very windy the night when Yuki rearranges the world, which turns out to be the source of that wind. The next day, half of Kyon's class is sick (and they have been for days, but they were fine yesterday). Guess what the Japanese words for "cold" (the disease) and "wind" are. They're both "kaze."
Itsuki first notes in Sigh that big trouble is brewing if he stopped blithely smiling at everything. When does he first demonstrate this? If you watch the anime or read the manga, earlier in Sigh - he is beyond not smiling and legitimately worried when he catches Kyon's arm to prevent Kyon from punching Haruhi. It's more than hinted that he thought Kyon's actions would have caused The End of the World as We Know It.
The line Kyon shouted to Haruhi three years ago: "Sekai wo oonimoriagerutame no John Smith wo yoroshiku". What Haruhi's SOS-dan stand for: "Sekai wo ooini moriagerutame no Suzumiya Haruhi no dan".
The music video seen in the credits of early episodes is highly likely to be the one Haruhi threatens to make everyone participate in at the end of the series.
It's mentioned that the events of "Snow Mountain Syndrome" was the Cloud Canopy Domain's attempt to communicate with The Brigade, and perhaps make Haruhi do something. How is trapping people in a mansion communication in any sense of the word? But it actually makes sense. If you don't share a language with something and know absolutely nothing about it, then putting it in a closed, safe environment is the best way to study it and attempt to find some common ground. The mansion's ability to generate anything you can think of allows the inhabitants to feed themselves, so you don't have to worry about accidentally poisoning them or otherwise hurting them because you don't understand their needs. It's basically an ant farm.
In Remote Island Syndrome, a lot of viewers wondered if the murder was always fake. Was there originally a real one, and Haruhi retconned it when she realized that the only potential murderers were her friends? Kyon notes that this is wrong, as the murder was too convoluted from the start to be anything but a set-up. Fast-forward to novel 10, and Koizumi describes himself (and the others espers) as a "tool of Haruhi's subconscious." Haruhi did cause the murder mystery, but not directly. In empowering the espers, she created an organization that would act in her best interests without her having to move on her own. The same as a boss hiring some really good assistants.
Imagine being Yuki. Imagine being created with the one sole goal to keep things in order. Now imagine having to put up with all of Haruhi's crazy scheming, having to somehow restore everything to the way that it should be, every day, no end. Now imagine not being able to scream, or cry, or let out any of your frustration, because you weren't created to have emotions, and you're isolated, and you have no choice except to go along with what you were told, because you can't do anything to change it. No wonder Nagato wanted to change the world in Disappearance.