Warning: More spoilers.
So I've reviewed the movie and given my thoughts on the changes. This post will be devoted to some of my favourite moments from the movie.
1) Captain Pike: the movie prominently featured Captain Christopher Pike, the first captain of the Enterprise. Fans remember him from the original pilot of the original series before Gene Rodenberry made the second pilot that introduced Star Trek as we know it. Pike wasn't terribly different than Kirk, but I've always held a special place for him in my heart. It was good to see him in a movie, albeit played by a different actor. In the movie, he's an important factor leading to Kirk becoming captain of the Enterprise.
2) The red ensign: a long-standing joke about Star Trek is the unfortunate "red ensign". Whenever an away team beamed down, it consisted of people such as Captain Kirk, Spock, Dr. McCoy, and an unknown character of low rank wearing a red shirt. More often than not, this character died violently. The writers of the movie purposefully and humorously provided a blatant "red ensign" moment. Captain Pike orders a space drop (sky diving from orbit). Reporting in drop suits are Kirt, Sulu, and some guy dressed in red that has made no previous appearance in the movie. His name was Ensign Olsen, or something like that. He was amusingly gung-ho about kicking Romulun ass, and the movie makers introduced his character in a way that you just absolutely know that he'll be dead in a few minutes. And what do you know: he pulls his chute too late, breaks his leg when he lands, falls over the edge of the drill, and gets sucked into jet of flame underneath the platform. I've never laughed so hard at such a horrible death.
3) Scotty's question about the future: Kirk and Spock Prime arrive at the lonely Federation outpost on the ice planet that Spock abandoned Kirk on. They find Scotty, and in the course of their discussion, it is mentioned that Spock Prime is from the future. "You're from the future?" Scotty enthusiastically asks. Spock Prime answers in the affirmative, to which Scotty, who clearly doesn't believe Spock Prime, asks, "Do they still have sandwiches there?"
4) Spock loses it: I mentioned this part in my review, so I won't go into detail. Kirk needs to take command over the Enterprise from Spock, using a regulation stating that someone who is strongly emotionally affected by the situation should be removed by command. Kirk antagonizes Spock, accusing him of not loving his recently-deceased mother, and Spock goes absolutely ape-shit, beats the tar out of Kirk, and only stops choking him when reprimanded by Sarek.
5) Ringtone: Near the beginning of the movie, when a young Jim Kirk steals his step-father's antique Corvette, his step-father calls Jim on the car's phone. The ringtone is the same annoying ringtone has been used on cellphones for years now. "Do-do-do-dooo! Do-do-do-dooo! Do-do-do-doo-doooooooo!" And the phone is a Nokia. Nice to see that Nokia will survive World War III.
6) Breaking the tension: After the beat-down Spock inflicted on Kirk in point number 4, the bridge crew stands around in an awkward silence. Scotty looks around with a wide-eyed expression, and then says, "I like this ship! It's very exciting."
7) Spock/Uhura romance: There's an episode of the original series where everyone is hanging out in the mess hall. Uhura starts singing a song, making it up on the spot, about the Enterprise and it's crew, and there's a verse about Spock that she sings directly to him. That's the most intimate moment between the two of them I can think of. The writers of the movie seemed to take that small, brief spark and run with it. I was surprised at first, and didn't really know what to think, but I eventually decided that I like it. I especially liked the look Kirk gave them when he realized that the two of them were a couple.
8) Kobaichi Maru: I have no clue if I spelled that correctly. It's the test in Star Fleet academy that was designed to be a no-win situation to see how cadets would react to it. It turns up in Star Trek II: The Wrath of Kahn when Savik takes--and unavoidably fails--the test at the beginning of the film. As the movie goes on, it is said that Captain Kirk is the only who ever passed the test. Kirk finally explains to his son, David, that he reprogrammed the computer to change the variables of the test. In other words, he cheated. It was nice to actually be able to see that moment, especially when it is revealed that this is how Kirk first meets Spock, who is the designer of the test.