I recently finished my first game of GalCiv3. All DLC, normal difficulty, huge galaxy, tech victory, overall strategy of peaceful annexation (conquered only the mega-event Dread Lords world), 442 turns, score 127. I could have finished much earlier but delayed the too-easy tech victory for some time. As I played, I jotted down notes about various aspects of the game that I felt could be improved.
1. Shipyard defenses. Shipyards are easy to replace if destroyed, but it'd be nice to be able to build better defenses and weapons for them (with constructors) to avoid the annoyance of guarding or rebuilding them. Or perhaps they could be attached to an economic starbase on a neighboring tile, so that enemy ships would have to destroy the starbase to attack the shipyard (or destroying the starbase could also destroy the attached shipyard).
2. Civ info on trade/request screens. It'd be nice to be able to view stats and diplomatic info on civilizations when their leaders offer trades or make requests.
3. Change minor races from immune to culture flip to highly resistant. They should be resistant enough that annexation requires significant time and effort (building an embassy and cultural building on nearby worlds, building an influence starbase, taking influence bonuses, etc). Or perhaps instead provide a peaceful manner of convincing them to join your civilization through high-level diplomacy. Something other than outright conquest.
4. Better A.I. world-building. The A.I. seems incapable of effectively taking advantage of the adjacency system. Whenever I annexed a planet, I had to rearrange (demolish and rebuild) two-thirds of the world to get good adjacency bonuses even when purposing the world to the same primary function (economy, manufacturing, research) for which the A.I. seemed to have been using it. The A.I. does things like build plants (solar, fusion, quantum) on the outskirts of a group of factories instead of the center, build isolated farms instead of clusters, etc.
5. Tool tips for each type of treaty and alliance on the tech screen. Self-explanatory.
6. Dual- and tri-constructors should be standard models and used by the A.I. It's efficient and logical for the player to build constructors with multiple modules, but it feels like cheating because the A.I. doesn't do it. Also, the A.I. doesn't seem to upgrade its starbases much if at all.
7. Change one-per-galaxy buildings to one-per-player. Subjective preference. I imagine some players might enjoy the race to get these buildings. I tend to think they require too much familiarity with each tech tree to be enjoyably pursued. At the very least, the player should be notified with a pop-up if another civilization completes a one-per-galaxy building.
8. More unique dialogue. Requests and other lines could be unique, tailored to each civilization, hopefully avoiding being stereotypical to the point of comedy. A little humor is good, too much kills the mood.
9. A.I. should decommission economic starbases when losing a planet, or the player should gain control of those starbases (and shipyards). I got around this by trading for relevant starbases when I annexed planets, but it seems odd to have to do it.
10. Tech victory is too easy. A tech victory should require researching the entire tech tree. "We must understand everything else to understand this." Or maybe the ascension techs themselves could be much more costly. It just seems far too easy right now.
11. Economic victory. There should be a proper economic victory. Give each a civilization a "buyout price" based on their number of planets, starbases, and ships, population, diplomatic disposition, etc. Make it late-game, but make it possible. It'd be an extension of existing mechanics: I essentially bought-out a rival by purchasing the majority of their planets. An easier way of implementing this might be to make homeworlds purchasable at an inflated price if they are that civilization's last world.
12. Trade value for mined resources seems too high. Late-game I was able to buy several worlds at once using only mined resources in trade. I like having an economic option, but it felt just a bit too easy. I don't a want a major nerf, tho, just a minor adjustment.
13. Show remaining ship moves on the 'corner card'. It's a minor annoyance to have to hover the cursor over a ship to see its remaining moves.
14. Ability to specify initial shipyard location. Yeah, it's a minor gripe, but still. 
15. More hitpoints for starbases as they're upgraded. Maybe 10 points per upgrade? They do get bigger as upgraded, after all.
16. The shades of green used by Thalans and Torians should be more distinct. At times it was difficult to distinguish their ships at a glance when zoomed out.
Btw... Good game! I enjoyed it and will play another galaxy on a higher difficulty when the next expansion or significant patch is released.
I'll also take this opportunity to say thank you for releasing this game on GOG. I wouldn't have played it otherwise (I don't use Steam), and I appreciate it. You rock! 