WARNING: CONTAINS SPOILERS!
Where do I start? Probably right at the beginning, where all of Star Trek history is ignored and the Enterprise can now magically fly through the atmosphere, land, and go under-water. Now this isn't just a result of this being an alternate timeline, as the technology can't just materialize out of nowhere, and TNG demonstrates that even a hundred or so years later in the normal timeline, Troi still can't land the Enterprise D on a planet. In fact, one of the big technological advances in the Star Trek universe is when Voyager comes along and, being a much smaller ship, now has the ability to land on the surface of a planet. But the much older original Enterprise having this capability well before the technology was established as having been developed, ridiculous.
Look guys! I'm a submarine! Wait, no, I'm a spaceship! No! I'm a fish-bird-ship!
Speaking of ridiculous technology, what's with the transporter device that Starfleet has that can transport someone to the other side of the galaxy? Why keep building ships if you can just transport things from one place to any other, with distance not being a major factor? Now that the technology exists, it would be insane to not utilize it all the time. It was a crutch the writers utilize without thinking about the consequence of such a technology existing, as now any other means of transportation is a stupid waste of time and energy.
I probably could have gotten over those two things, but the everyone-is-in-danger-of-dying-action-scenes to character development and story ratio is pretty sad. The movie seems to just jump from one action scene where characters are in danger of dying to another action scene where characters are in danger of dying. There is very little downtime between these action scenes, and by the end I was quite bored with the improbability that the crew members would survive so many back-to-back near-death scenarios. I think Spock almost died about 76 times during the movie and Kirk almost died 483 times. When nearly every single scene is a life-and -death situation, it just ends up cheapening the danger and they all turn into a bland mishmash of over the top action.
One of Star Trek's most beloved tenants and the driving force behind Starfleet, The Prime Directive, is what makes the Star Trek universe what it is. Yet at every twist and turn, the writers like to point out how much they enjoy violating it. Spock claims to obey it (not be seen by the primitive society), yet the very first scene has him jumping into a volcano to stop it from exploding (you know, interfering with a primitive culture and events, which violates the Prime Directive). Don't get me wrong, I'm not forgetting Star Trek: Insurrection where this very same sort of interference occurs (along with many instances of violations in TOS and subsequent series), but since the writers make a point of Spock logically and calculatingly adhering to policy (as he claims in the new movie), it doesn't make sense that he was even willing to participate in the first place, as he was under no pressure or strain, yet chose to violate the Prime Directive anyway (contradicting his claims of following policy).
These are just a couple of the things I found lacking and many things were just absurd (Spock's "KHAAAANNN!" moment was so cheesy it almost made me laugh out loud, yet I think they intended it to be dramatic and poignant). I know that it seems I'm nitpicking, but add up all the problems with the new movie and you end up with something that is Star Trek in name, but lacks all of the spirit and characteristics that made the show what we loved. J.J. has shown his true colors as not being a Trek lover by Michael Baying the movie. I hope Star Wars takes up all his time and that they get someone who really cares about things like story, character, and the Star Trek canon to make the next movie. With that, I'll leave you with this picture of a completely useless and meaningless character who was added as a non-essential plot device, but looks good in her underwear.