I'm sure a lot of these things will have already been said, but here's some loose thoughts on what I'd like to see:
1. Claimable and useful Gas Giants. Perhaps like a research/other version of Asteroids?
2. A more interactive/developed U.P. system with some kind of resolution proposal mechanic using selectable parameters (drop down menus?)
3. All the diplomacy options we saw in GC2 and many more - 'Vote with me/against Lord Kona at the next UP Summit', 'lend me money/ships/research/other'. Mini objectives generated for and by the AI and human players (a la Rome/Medieval TW) could be implemented through diplomacy too. 'Kona, go do! Get big bag of goodies (automatic) upon completion.' If kept simple and rare enough (not every 5 turns), it could be fun.
4. Individual unique ship names that the AI will use too: i.e. USSC Discovery 1, ISA Excalibur, EAS Agamemnon, USS Defiant, Nostromo, Axiom, etc instead of 'Drengin Cruiser M1 - 2372' - Possibly only for medium and above size ships?
5. Modding tools that include an in-game map, empire and generally everything editor. I'd be happy to wait a few expansions for that. Think Twilight's tools, only better and more integrated. Easier modding means more modding which means a more lively game community.
6. Ability to customize and save starbase appearances without leaving the game.
7. As nice as it is to discover Xeno Ethics on your 10th turn, the creative ability bonus as was in GC2 could use a tweak/nerf. Even at half the chance of it happening, it would still happen too often and I would even say that it might be an idea to disable it completely for multiplayer for the sake of balance unless there is a total rework planned for it.
8. Planetary invasions should feel less like 'whack-a-mole' and more like a planetary invasion. We have invasion methods (propaganda, gas, etc), why not have a planetary 'defensive posture' mechanic? 'Guerrila Tactics', 'Hold the line', etc all having bonuses/penalties against the various types of assault. Dunno... just needs more depth I guess.
9. Stable/Unstable Wormholes. All temporary but duration random with some being one-way tickets and others having no exit (bye-bye ship)
10. AI that doesn't declare war on someone with 3 large enemy (at war) empires in between.
11. Make space feel bigger. Even the small map needs to feel a bit more 'epic'. One of the reasons I've always played GC2 with each empire having a -400 modifier to their range ability is because even on the biggest map, it doesn't take you long to be able to go pretty much anywhere. New space terrain and mechanics or no, it still feels like there's a lot of clutter on the map. The nebulae penalties are a nice touch though.
12. Bring back Jenna Casey