...Chekov, a former security chief in TMP, didn't know that weapons fire would set off the alarms.
Might have been a new system, though. We never got alarms when phasers were fired in TOS ("Conscience of a King" or "The Changeling" for starters), and the movies didn't feature hand phaser fire in the corridors so we wouldn't know one way or another.
Perhaps the new alarm system is what allowed Starfleet to move the weapons from dedicated armory vaults to simple cabinets on the walls of communal spaces?
No excuse for Uhura not knowing Klingon, tho. And I'm not sure one would be needed. How many USN radists during the Cold War spoke Russian? How many spoke German or Japanese in WWII?