While there are lots of expantions that could be made to the game, the main thing I'd like to see at the moment is some actual reason to visit other systems, one reason why I thought the courier mode was such a good idea.
At the second you can pretty much just hop around the same sectors and make money, and while there is a huge variety of stellar objects, other than the special locations for missions there isn't a lot of point in exploring for the sake of exploring, since you can generally find rich resources or asteroid fields kicking about somewhere.
I would also like to see the cash worked out a little, in the later game, since currently as I can't complete that bloody mission I'm pretty much just grinding cash to get enough to buy a moon as that is something I've not done before.
While robotic miners are awesome, it'd be nice to get some more addons to your ship that facilitate making more money, EG cargo expansions, or maybe owning factories.
I also at this point am not exactly sure what more I can do with my ship, since the gecko is pretty damn awesome, and while there are a couple of bigger ships out there, even the anaconda doesn't seem as good.
Then again, I still have to work up enough kills to get to elite rank, assuming I can't solve the mission problem, so I'll still have plenty to keep me busy.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)