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First, Kerrigan had a really crappy past, to the point where she would be considered a Woobie if she hadn't become the Big Bad of Brood War.
Secondly, the infestation process is explicitly stated to remove one's humanity and morals, among other things. Basically it knocks Kerrigan's ethical principles back to that of a child. And what would happen if you gave an abused child an insane amount of power? They might use that power to lash out at the people who hurt them. In this case, the universe. Adding to that, her lack of morals would have made Evil Feels Good.
It was mentioned that Kerrigan was infested to give independence to the Zerg swarm. But throughout the campaign Kerrigan was basically falling in like with the Voice's bidding. This means that the Overmind's plan failed, and the Zerg swarm is still as trapped in its programming as ever by the voice.
Kerrigan likely thought that Jim had abandoned her on Tarsonis, just like Arcturus. She didn't know that Jim did try to save her (and failed), nor that he left the Sons of Korhal shortly after because of her betrayal by Arcturus. So at the end of Starcraft II, after she gets zapped by the Xel'Naga artifact, seems to regain some sense of humanity, and is rescued by Jim, she realizes that in reality he did care about her (hence her confusion when she becomes slightly lucid), adding to the Crowning Moment of Heartwarming of it all. Though seeing as the upcoming sequel focuses on Kerrigan and she still seems to be part zerg, it doesn't look like she's going to become a straight hero or reverse all of her character development, maybe become something like a type 3 or 3.5 antihero.]]
A mission in the protoss mini-campaign has a part where you rescue protoss who were stuck mid-warp in time-space due to pylon power being cut off. Just imagine what would have happened to them if Zeratul never restored power...or, for that matter, imagine that happening in any multiplayer game where a player manages to destroy a pylon field before units manage to finish warping in...
At first, Hanson's side missions might seem pointless, but in reality, they aren't. When Raynor got the call for help, they were in exactly the same position that Kerrigan was in during the Fall of Tarsonis (thrown under a bus for expediency and in danger). Raynor already knew what it was like to fail to save one person from that fate, so he could not simply leave these people to the same fate. It's also why he sided against Selendis; the last time he gave up when there was still a chance, Kerrigan became the Queen of Blades and the results were completely tragic. Raynor probably believes that if he made the choices he failed to make at Tarsonis, then he can gain solace for failing to save Kerrigan. Alternately, the colony of Agria is in essentially the same situation Mar Sara was at the start of (vanilla) Starcraft. Abandoned by their government with just a rebel force to help them out of their plight.
Likewise, the "zerg were corrupted" plot twist seems random, but considering that Duran was manipulating them back in Brood war and already served an ancient being with goals involving the Xel'Naga, it actually makes perfect sense.
Most people dismissed the fact that the news was all live as Rule of Funny. But there's something from the novels that needs to be kept in mind: The Confederacy ran very heavily edited news posts as fact for a long, long time. Merely passing a law that all news broadcasts must be live would make Mengsk look pretty good. To take this even further, Kate's occasion pro-Raynor or Anti-Mengsk comments actually make Mengsk look good for allowing them. Donnie's clumsy attempts to cut her off even seems like playful banter the audience may enjoy as much as we do.
The ending cinematic:
At the ending cinematic it's revealed that Tychus was working with Mengsk in exchange for his freedom, and to earn it, he needed to kill Kerrigan. However, before doing so, he lets the laser of his rifle be seen by Raynor, which seems like a rookie mistake. But if you pay attention to some of the cutscenes between missions, you can tell that he tried to internally justify his actions as being a favour for his friend. It's only when he sees Jim interacting with Kerrigan that he's convinced that he truly loves her, which is why he gives him the chance to save her. This also explains why in Heart of the SwarmRaynor doesn't seem to hold a grudge against him.
Another bit: When Tychus initially accepted the deal from Mengsk—heavily implied to be "kill the Queen of Blades to secure your freedom", he didn't know any of the backstory regarding Kerrigan and Raynor. He just thought he was going to be risking his own life to kill a threat (in exchange for his freedom if he succeeded), which, despite what he saw as a low chance of success, certainly beat rotting in prison for the rest of his life, especially if he could spend that time with his old friend. It wasn't until he learned that backstory, and realized that Raynor still cared about Sarah, that he started having his misgivings. Indeed, he tried his best to avoid the position he was in at the end of the game, including trying to convince Raynor to cut and run at one point.
Anyone playing the game a second time around and watches all of Tychus's interactions with Raynor takes on a whole new meaning. He was only ok with the idea of shooting Kerrigan when he thought she was just the "queen bitch of the universe". When he found out that her death would not only mean breaking the heart of his best friend, but also end the known universe, he does everything he can to stay the hell away from Char until the last possible moment. He even screams at Raynor that he threw several years of his life away for him, and now Raynor is literally asking him to throw the rest of it away too. In the end though, when Raynor asked him to stand by his side one last time, Tychus still complies, with a grim look of resignation on his face because Raynor didn't take the hint (He obviously couldn't tell Raynor the reason out loud).
A simple, subtle bit of brilliance. Protoss often greeted with each other with the phrase "En Taro Adun" during the first game and the Brood Wars, but after then they switched to "En Taro Tassadar" to honor their most recent hero. Immortals, however, show their age by still using "En Taro Adun."
A couple things about the missions you do for Dr. Hanson:
The entire mission branch is Kerrigan messing with Jim. Terrans are of no interest to the Swarm except as cannon fodder for important missions (with the exceptions for powerful psychics of course) so there's absolutely no reason at all for the colonists to be attacked and have such a persistent infestation unleashed on them as anything other than a distraction for Jim. Kerrigan is using them as a distraction to keep Jim busy while she searches for the artifacts as well as to demoralise him. This makes sense with a few other things in mind: while the order you do things in can greatly vary Kerrigan gets really annoyed at Jim after the first few artifact missions, noting how he keeps interfering and doesn't know when to quit so it makes sense she'd whip up something to distract him, and second there's Haven's Fall, Ariel's infestation suggests a sadistic higher mind at work. She's been left self-aware and her mutations are too clean, not something that Terran infestations generally have since it's considered an inefficient use of the Swarms resources to compensate for Terran's many genetic draw backs. Infested Ariel is a personal message from Kerrigan to Jim.
Kerrigan was aware of everything the Raiders were up to via the zerg specimen sample in the lab. It's growing rapidly and is in a position to oversee the collection of the artifacts and overhear everything Jim learns from Zeratul's memory crystal. This would explain how they've managed to keep it contained for so long (Heart of the Swarm demonstrates repeatedly that all Kerrigan needs to do to free zerg from containment is to simply will it hard enough)with only half-hearted attempts to escape confinent via releasing acid into it's containment jar when it could simply use it's tentacles to smash the jar. One wonders if maybe Kerrigan was deliberately allowing Stentmen to study the specimen in the hopes he'd mess up r discover something she could use.