So after playing GalCiv2 for awhile (love the game so much), there some things that could have been done differently that if not implemented to 3 right now, I hope they will be. Since alignment has been discussed a lot, I won't bring that up 
Extensive Government System: As much as Imperialism, Republic, Democracy, and Federation simplified things in the game, I'd like to see a more extensive government system. One that allows the player to adjust the policies of his empire, whether making things more tyrannical or more democratic for your people.
More strategic warfare: Something that Civ5 realized was the whole using the unit with the bigger number got old, thus they changed to a more tactical form of gameplay for warfare. For GalCiv it'd have to be a little bit different than Civ5 because of the fleet mechanic, but here's how I'd do it: Counters. Corvettes or Frigates counter fighters and bombers, bombers counter larger ships, fighters counter bombers, larger ships counter smaller ships, etc.
Auto upgrade: I really hope I'm not alone on this, but the whole scenario where designs upgraded themselves but YOU had to upgrade already built ships was a chore. Personally I kept from building any navy until I had researched some of the stronger techs, or I was at war. Thus, simply put, if you still have the whole Mk# situation for ships PLEASE put an auto upgrade system ingame.
NO DREAD LORDS FOR NON-CAMPAIGN GAME: I cannot stress this enough, having the Dread Lords randomly appear in the non-campaign version of the game was a poor choice. They're pretty much overpowered and if they appear before you have the technological capabilities to fight them, you're pretty much screwed. The whole point of that version of the game is an empire building sim. We don't want to worry about some mystical precursor race appearing out of nowhere to f-up our empire, we have enough problems with the other races. Considering what you're doing story wise with the game I'm assuming we won't see the Dread Lords or the Arnor at all in the game, so I'm not too worried about them appearing specifically in the main empire building game, but it applies to anything else that could essentially be an endgame scenario when you're nowhere near able to be ready for it.