Got the game ca. 2 weeks ago, want to give a bit feedback too. So far it's limited to certain aspects, mostly handling/interface since I have not played soooo much yet due to lack of time. Also, I guess I don't have figured out everything so some "issues" might just easily go away once I get a better hang on this 
But here we go.
1. General Impressions
Everthing looks way more shiny than in GC2, which is great. No stability issues so far, not even a single CTD. Things I miss: easy quick save option, option to take screen shots (or is it there somehow?) and a real time clock in the UI 
2. Ship Designer
Most impressive. Designing own ships was nice in GC2 already, but being able to toy around with offsets or to manipulate objects' XYZ axis independantly is just great.
Only one prob: use of middle mouse button to turn the view around is IMO both counter-intuitive and uncomfortable. I guess like me many ppl I use a mouse with "clickable mousewheel" instead of a "real" middle btn and I think it does not work too well (tested even my second mouse, wasn't better).
Pls. add an easy alternative, like right mouse btn use or even some UI elements.
3. Map
- I miss the somewhat bigger Civ logo for a civ's main planet/home world (compared to other colonies) on the map.
- Not sure if I should be able to see other civ's rally points? Esp. when my scout/survey ship moved out of sensor range again.
- I had one issue with a ship "disappearing", it was still displayed in the UI list, but no icon visible anywhere. Turned out when I set a move target somewhere it came out of a field of asteroids. IMO would be better to have the icon always on top, regardless of "terrain" below
-Speaking of icons, I find those for nebula are somewhat confusing, as they look similar to asteoids when zoomed out, but maybe that's just me
- What I didn't like in GC2 was that sometimes useful stuff (resources, planets) was clustered in one area, with way less in others. Regardless of difficulty level this often meant either a rather easy game or a pretty tough one dependign whther you started near such a cluster or not. Wondering whether this is the same in GC3 because I had two black holes next to eachother and quite many of resources nearby. Maybe on map generation there could be options for more or less balanced distribiton.
- If there's some eye-candy still to come, I wonder if we get planetary systems with planets evolving around their sun(s), planets with real ring systems and may be some other stuff besides black holes, asteroids and nebulas. What is there right now looks really cool though, esp. in close-up views
4. UI
Sometimes I wished certain things were easier. Example:
To cancel a building or ship in the qeue it has to be selected to hit "cancel" = usually two mouseclicks. Could we just get a "close" icon (like the Windows x) after each entry in the qeue? Or simply use right mouse btn here too?
Also, when you rush stuff, then cancel it, you should get the money back? Otherwise it's just lost.
Back to streamline usage - it's seems generally RMB is never used. Is there a specific reason for this? IMO RMB use could improve a couple of things, like above.
Ok, that's all I can think of now. More later when I played more 