Not that these things are gone in the new movie, but somehow there is still more of the old charm back. The dialogs of Spock and Kirk really fly and I loved all the twists they did on the old Wrath of Khan movie. Like that it is Kirk who dies in the warp core and Spock who rescues him (even if the blood thing was a bit contrived considering that there were 72 other samples of superhuman aboard).
And of course Benedict Cumberpatch who was esssentially playing Sherlock was a wonderful villain. I really enjoy it if the bad characters have proper reason and motivation for their actions and are no muahahaha EVIL. I also liked the ambiguity of the new federation. It's now all as clean and easy as it used to be and it gave Khan a real good reason to be pissed at them.
It also makes a lot of sense that the absence of Vulkan makes a huge difference to the federation's foray into space. I'm looking forward a lot to what they do with the klingons in this versions of the verse. I presume they will play a huge role in the next movie.
The Kirk/Spock ship is soaring like a huge banner all over the place. And I love it to pieces but it also makes me want to talk about the gender aspects of the ship. Because it's attractiveness really comes from those two superinteresting and well formed characters getting closer and closer to each other. And it always makes me feel bad for the tv-women, because the reason say Spock/Uhura will never be that interesting is that the female characters just don't get that sort of dept and are consequently not as interesting for shipping. And Star Trek has the excuse of K/S being THE ship on the Enterprise but so many modern shows and movies have this exact problem that the female characters just don't get to have that many edges, not even the leads.