Let me first say that I am happy to have another movie. Like many other ST fans, I also wish we had more in-depth story, even if it means we have to sacrifice some action and special effects. However, as we all know, the new movies are geared more toward action and newer audiences, and less toward deeper more thought provoking issues, so I guess we will have to take what we can get. Some star trek is better than no star trek.
I enjoyed the action and I enjoyed the movie, since I knew going into this what to expect. I enjoyed the action because I knew I was going to see an action movie. I like the cast and the characters. I wish we could have seen more character development and the dealing with more contemporary social issues. But alas, I guess the younger crowds don't have the cognitive appetite or patience for drawing out anything substantive and meaningful. They just want it fast, loud, and in your face, and they want it NOW. They don't have the attention span for anything less (which is, I think, a criticism of modern day culture).
Also, I liked that Anton Yelchin appeared a lot in the movie. Its nice when supporting cast members get some character development, and especially Chekov given the recent passing of Anton.
In any event, just because I enjoyed the movie doesn't mean I can't be critical. So here is some stuff I thought didn't made sense:
How can the bad guy "camp" be so small and so sparsely staffed when later in the move we see literally thousands of them fly away in a swarm? Where were all the enemies when Kirk and Spock broke everyone out? And why do they live in a camp when there are clearly enough soldiers to support the economy and social system of entire city (families, agriculture, housing, infrastructure, etc.)?
I understand that a car with a transmission can be 'jump-started' by getting it moving and then popping it into gear, but how in the heck does that work with a starship warp drive and/or impulse engine? Is there a turbine that the rush of air caused to turn so that Sulu could 'pop' it into gear? There is no air in space, and a star ship is built for space travel, so this really doesn't make sense to me.
The whole flying around on a motorcycle was hard to watch. To comment on what DMD said, I can believe the independently moving holograms if they are being projected from those floating disks that we saw Jaylah deploy when she rescued Scotty from those thugs. Assuming the projector moves with the hologram, inside of the hologram, then I think it is feasible (I'm thinking of Ace Rimmer from Red Dwarf when he acquired his remote projector that allowed him to leave the ship). However, the idea of using a motorcycle successfully to take on the bad-guys in their camp is hard to believe. I mean, c'mon. Seriously?
I liked the Jaylah character, but I thought the movie would have been just fine without her. She was unnecessary to the story, and I think the time could have been better spent on the TNG crew character development. Also, I personally didn't like her accent. Sometimes it was cave-man style, and other times it sounded like a British accent. I was not able to buy into her character. Although, I did think she was quite easy on the eyes and I certainly didn't mind looking at her. Plus the whole you-killed-my-father thing is sooo old. It's like, were the writers even trying?
I didn't like the death of old Spock story. I don't remember seeing much character interaction between old and young Spock to be able to understand how young Spock felt. I guess young Spock was sad? He did seem very sad. But why? Did things happen off screen between films that we, the audience, are unaware of? Were they close? I suspect the writers may have thrown the death of old Spock into the film as a nod to the passing of Leonard Nimoy. Which is fine, it just didn't feel like the loss was deep (other than being reminded of the passing of Leonard Nimoy in real life).
How exactly did the loud music make the enemy ships explode? I can understand that it may have jammed their signal from ship to ship so that the swarm becomes un-coordinated, but I don't understand how that made them spontaneously explode?
I agree with forst, I did not like the fountain-of-youth mechanic because it also reminded me of Insurrection, especially since staying young involved sapping the life of other beings (which I believe was also present in Insurrection, but I haven't seen that movie in a long time).
That's it for now. I plan to watch it again soon, so I may have more to comment.