One might expect all the low-ranking trainees to quickly fall in line when their high-ranking instructor arrives (as opposed to just lounging around in a <shudder> civilian fashion). That line could simply have been outside camera view.
Regarding the terminology, somebody being trained to be an enlisted crewmember wouldn't be called "cadet". Nor, in today's parlance, would somebody who has already got her commission to Lieutenant (jg) and is merely taking a postgraduate command exam. Yet somebody in that test was considered a cadet. Who was that?
We saw the jumpsuit folks, who might have been enlisted trainees or then already trained little helpers for the instructors, or then a mix of both. We saw the regular heroes serving as instructors' helpers. We saw Spock who apparently was the instructor. We saw Kirk who was a higher-up instructor, possibly Academy Commandant. And we saw the two new officers, Saavik and Cray, both of whom apparently were already graduated and commissioned since they wore the uniforms and the rank pins. So again, who was the cadet?
To be sure, nowhere in the movie is Saavik addressed as cadet. She's "Lieutenant" or "Mister" to Kirk from the beginning to the end.
To add to the oddity, Peter Preston whose "Engineer's Mate" designation suggests he is an enlisted man is called "Midshipman", a term traditionally interchangeable with cadet or referring to cadets on shipboard training, and thus not applicable to enlisted men at all. If Preston is in fact a cadet/midshipman, and destined for officer commission, then perhaps some other people in jumpsuits are also cadets/midshipmen and not enlisted trainees?
This would be supported, strangely enough, by ST:NEM, where cadet Picard in an old photo wears the ST2 jumpsuit. What's more, he wears it with the black collar that the costume designer wanted to denote enlisted status. Apparently, the costume designer was wrong...
Timo Saloniemi