There's no dedicated Forum for audio, so I guess this fits under the Art category (as a musician myself, I'd call anything audio-related an art form), so here goes.
First, I want to say that this game has some of the greatest orchestral music I've ever heard, anywhere. Was it done with MIDI, or a real orchestra? (Seriously. I do want to know. I'm terribly curious.) In particular, the theme music that comes up when I first log in would work just fine as the opening music for a new TV series.
Second, I think it might be fun to have some optional "shipboard chatter" when we're aboard and flying around. A lot of this can be related to DOff Assignments; for example, when a Sector Assignment is done, a background voice can announce, "[Department] Team has returned from a successful mission." If an Assignment ends with an injury, a voice can say, "Medical team to [Department area]." (A Sector Assignment with an injury would send the Medical team to the transporter room.) Another possibility would be ETA updates and similar information when warping through the galaxy. I'm sure others can come up with more, including just random remarks when there's too much silence.
(And the reason I say "optional" in the above paragraph is because I think this is something that players should be able to shut off if they don't want it.)