The Single Biggest Mistake Each Star Trek Movie Has Made
11. Star Trek III: The Search For Spock - Boy's Club
The Mistake: Uhura doesn't join the mission to Genesis.
Why?: Well there's the question, isn't it? Uhura is very clearly on-board with the mission to recover Spock's body. In fact, she plays the long game, taking a position in a lonely transporter room so that she can help get the crew aboard the Enterprise. Then, nothing. She says that she will meet them at the rendevous on Vulcan and she exits the film until the finale.
The novelisation goes much farther toward explaining this. Here, she remains behind so that she can scramble any messages being sent about the Enterprise. She does the same for the Excelsior as a personal attack on Captain Styles, who she felt usurped Sulu's command. Once this is completed, she runs to the Vulcan embassy and seeks asylum from Sarek, which he grants.
That is an excellent explanation as to why she remains behind, though none of this is in the film! Also depicted, she hits energise and the audience is left to assume she either threatens 'Mr. Adventure' beside her into not reporting her or finds another way to cover her actions long enough to make it to Vulcan.