Okay, here's my thoughts on various aspects.
Prepare for a biased love-fest, in the family-friendly sense
The Cinematography and Design
This was a fresh approach to Star Trek, with dynamic camera movements, and a strong visual style that conveys the idea of a "bright future" in a very literal way (lens flares).
The visuals were absolutely stunning in terms of the VFX and design work, and although a departure from Berman-era Star Trek, was very pleasing to the eye, and conveyed a sense of reality. I was drawn in very much by the general look and feel.
The designs for the Enterprise, Kelvin and Narada were great, IMHO, and served their roles in the story nicely. I wanted to go back and soak it all in again.
The Sound Editing/Mixing/Design
This is one of the strongest elements of the movie, with many nods to TOS, and proving that those sounds could work very well to flesh out the Star Trek universe on screen.
From the was starships jumped to warp (BOOM), to the sonar pings heard right in the beginning, to the ambient sounds on the Enterprise and Kelvin Bridge, everything old and new worked perfectly together.
Story and Characters
The new writing team NAILED the characters, IMHO, making the both familiar and fresh, giving each character a fitting introduction.
The Alternate Reality provides an elegant solution to the problem of making an origin story work with the new crew, and to allow the changes necessary for the big screen, and as a bonus, makes the future unwritten, so anything can happen. IMHO, a masterstroke.
Leonard Nimoy provides a way to pass the baton, and the humor and fun makes the movie more of a joy to watch.
The Score
Michael Giacchino's score worked extremely well, and has grown to be one of my favorite recent movie scores.
TWOK, TMP and TFF scores are still favorites, but this score stands on it's own terms, and reflects the stylistic change from the old to the new.
I should also note that the score was criminally underrepresented on the Soundtrack CD, which omitted some fantastic key music cues, such as:
- The preperations at Starfleet in the hangar bay, with Uhura transfering to the Enterprise and McCoy sneaking Kirk on the Enterprise shuttle.
- The sequence where Pike takes the shuttle over to the Narada, and drops off Kirk, Sulu and Olsen.
- The platform battle, with Sulu's hero shot, Olsen dies red-shirt style and they disable the drill.
- Spock beaming down to rescue the Vulcan Council from the Katric Ark thru to Amanda dying at the start of transport.
- The sequence where Vulcan is destroyed, Spock notes that he is a member of an endangered species, and Uhura and Spock are in the turbolift.
- The cue for the monster chase on Delta Vega.
- The cue for Kirk and Scotty beaming up, as spock says "Live Long and Prosper".
- The cue where the Enterprises emerges from Titan.
Nods to TOS and Trek Lore
This was done in a fun, but reverent and fluid way, from lines of dialog, to bits of background business, to easter eggs, such as the Tribble in Scotty's Lab.
This film got so much right, IMHO, that could have easily gone wrong.