To all the old fans, Spock is the Smartest Guy Ever. The new fans will remember him as "Guy who lets billions die by dropping a decimal point." Way to characterize.
There's an attitude to the Old Kirk and other heroic ship commanders. If someone's going to be saving the world regularly he needs to be a serious badass. If Old Kirk was dropped on a strange world and attacked by a monster he'd improvise weapons from his survival capsule, or lead it into a trap, or run with a determined expression while looking for something he can use as a weapon or trap. Screaming and flailing arms while running is what the comic relief does, not the badass hero. No complaint about the actor, he did what he was asked to do well. But the writers either don't like or don't understand what a badass starship commander should be.
The lack of badassitude could be blamed on Kirk growing up without a father (thus losing out on paternal advice such as "Never try to outrun a cop with a vehicle over two centuries old"). But Old Kirk wasn't the hero because he was Kirk, but because he was the badass who could pull victories out of any unlikely situation. New Kirk got lucky once. But if we can't count on him to beat barroom thugs or a polar bear, how can we have faith in him beating bigger foes?
Meanwhile Spock, commanding a shipload of cadets in a major crisis, hands over the con to 17-year-old Chekov so he can rescue his mom instead of delegating that to a security landing party. Court martial, dereliction of duty. Chekov abandons his post to take over a transporter technician's job without handing over the con to anyone. Court martial, dereliction of duty, two counts.
The movie made a Big Deal over Uhura's skills up front. So they were telling us this to make sure we'd believe it when they showed her doing something amazing, right? Such as translating Romulan transmissions when Starfleet's computer can't handle more than a century's worth of dialect drift? Well, maybe in an early draft of the script. But somewhere along the line was the production meeting where someone asked, "If Uhura's not doing much in the second half, and this Nurse Chapel doesn't do anything until the hurt/comfort scene, can't we rewrite them as one character?"
Is there any other good explanation why Christine Chapel wasn't one of the characters carried over from the original series?
I miss Professional Uhura more than Chapel though. She got through the original series without ever being rescued. She could fend off attackers with a quip or a water pitcher. Or, after vamping Mirror-Sulu, with a knife. There were glimpses of her personal life--singing as a hobby--but we never found out her first name. She was an officer, doing her job. Now the reboot has her as the Love Interest. That's a big loss. It also rubs in that the reboot has no women in leadership roles. Even the board of admirals judging Kirk was all male.
Pike appointing stowaway Kirk as first officer is a plot contrivance on the level of "Antigones pursued by a bear." May not make any sense but the whole story collapses without it.
As for Scotty's last-minute technobabble save--that's the best they could do?
I'm hoping they make more Star Trek movies. With a clean slate they can tackle some great stories. But they didn't reach the full potential with this one and I'm hoping they do better. There's good precedent for it. The first season of Next Generation wasn't nearly as good as the later ones.