Can't say that I've noticed that the inside of my own carrier being particularly unkempt, although maybe that has something to do the choice of interior livery/colours I've chosen. I went with the one that I think is called "Mining" or something like that, because it makes the screens and monitors look kind of like the colours used by the LCARS system in TNG-era Star Trek.
Certainly I've come across plenty of big stations and outposts with more grotty-looking interiors than my fleet carrier. Seriously, some places are actually kind of disgusting with the amount of junk food wrappers strewn all over the place.
I have noticed the missing fan blade though. I agree that it would be a good idea if we could choose the level of dinginess for our carrier interiors. Ranging from utterly spotless and antiseptic, or slightly used with regular tidiness, or somewhat lived-in with non-litter clutter (pads, cups, clipboards etc), all the way to oh goodness imagine the smell complete with litter everywhere, dirty streaks and dripping water.