Indeed, Pike calls her cadet.
And a few seconds before that Spock refers to her as Lieutenant.
Makes sense. Pike shouldn't know her from Adam (unless he lets his eyes wander, that is), since she isn't part of Pike's regular crew, or even of Pike's replacement crew of cadets
. Even if Pike got an advance list of those cadets officially assigned to his bridge for the duration of the crisis, only Spock would really know who Uhura is and why she is aboard. And what rank she holds, because apparently her uniform type doesn't cater for any sort of rank insignia...
Her Klingon transmission wasn't even an important element since the Enterprise had a whole minute of free time to spare before they were attacked by the Narada after exiting warp.
Indeed. Sulu's parking brake incident was the real reason our heroes survived... Thanks to that, there was already a debris cloud in place to mask the arrival of the Enterprise
, with no less than two saucer halves marked "NCC-1621" standing between her and the Narada
As for Uhura's need for a solid CV, as opposed to the male heroes, there's some truth to it that she has certain standards to uphold as the only remaining female Trek character. OTOH, her job to begin with is one of the least glorious. Kirk commands, Spock does rocket science, Scotty tends to amazing machines, and Chekov supposedly does all three even better. Even Sulu, who could be compared to a truck driver, gets glory points for the nature of the rig he steers. But Uhura still remains the dimwitted automaton who could be replaced by a flashing "incoming hail" sign and nobody would really notice. Unless
her role is blatantly expanded from the familiar TOS one. Nobody else really needs the upgrade, as they are already up there. Uhura desperately needs hers.
And the movie delivers, sort of. It's the first time we hear Uhura might have language skills. Even if she's a single-trick pony, she now officially stands abreast with the other single-trickers in holding a nontrivial, even academic skill. Now, all we need is her doing something heroic and decisive (either with the skill or then otherwise) and she'll be on par in general terms. I'm just desperately hoping this "heroic and decisive" thing in the next movie won't include martial arts...