I enjoyed Spock's explanation when they were in the trade ship to both Uhura and Kirk about how much he does care. When they boarded the Enterprise again and she kissed him as a way of saying, this spat is over, it was very sweet because you could see it meant something to him.
Uhura seems like a private person. If this was Gaila she's be all about boasting about her Vulcan hottie but Uhura and Spock kept it a secret for a while and keep their relationship out of the public eye. Kirk got a look in because he is close to them both.
Maybe next movie you'll see them waking up in bed together one morning and the movie will have at last achieved an equal status with Star Trek's other most intimate relationship scene which took only 7 seasons to get to just that.