According to the ethics manual at my grad school, he should have asked someone else to make her assignment. Or she should have demanded it. As written, though, that was not a subordinate-and-superior conversation. I presume that she wouldn't have gone up to someone she wasn't dating and said: "You're putting me on the Enterprise."

She actually was skilled enough to get the position on merit. I felt like it just wasn't sufficiently acknowledged by the script.

Uhura dating Spock would have worked better if he hadn't been her instructor, or if the ethical issues had been acknowledged in any way. And also if she weren't the only major female character.