Heya dear Dev-team,
after playing the campaign, I've encountered some bugs I want to share with you. Also a little bit of feedback at the end:
Bugs:
1 ) When deleting a custom designed ship blueprint after the ship has been build, the icon vanishes from the fleet-overview. You can still select it, but the icon is blank (transparent)
2 ) Scrapping a building that can only be build once will permanently delete it. You cannot scrap it and place it somewhere else - its gone forever. This is true for both single items for the player and the galaxy. It does not happen for buildings that are "once for colony".
3 ) Some ideology-traits are broken, like the extra planets from the "blue" (harmony?) tree - the game did not spawn a planet on one of my games (which was already pretty advanced)
4 ) The "extra tile" ideology traits are not counting for future colonized planets, but just add an extra tile on existing ones. A simple workaround would be to give the player one extra terraforming-building.
5 ) I can add unlimited amounts of precursor-hull-strengthenings. While they still cost construction points, they do not weight anything. I guess, it would be better to just say, that it doubles the hull hitpoints (and maybe something like 25% general damage reduction?) and be happy.
6) After defeating an empire, their ships may remain on a planet, being stationed there and unable to be destroyed.
7 ) After upgrading a lot of starbases, the shipyard stopped producing constructors. I have the feeling, that it was after "1024" upgrades. 
Feedback:
a ) The ballistic option as offensive choice it inferior to missiles and energy weaponry. It has shorter range, less damage and the upgrades available are also a bit lackluster compared to the other two. (and even give you disadvantages) May need a slight re-balance.
b ) Starbases - phew, they feel like outposts, but not like the real big starbases from Star Trek. I spam half of the galaxy full of those things and only some really feel good (like an economy-based one with archeology-addition)
To be honest, there are too many starbases around. Reduce them to give them more of a strategical importance (similar to planets) but increase their abilities. There should only be two types of starbases: Military and Civil starbases. Military are the ones we have already, but may need a real boost in their ability to repel enemy fleets (remember DS9? That was a battlestation!) Civil ones should be capable to do everything else. From economy, to resource (also add ALL of the mining options for special resources, not just one so you don't have to build starbases in a 'creative' way around resources to get all the bonus-points from a specialization) and culture. Have fewer, but more important starbases.
c ) The bonus from a military starbase should also count for other starbases within its influence-range. Was not able to see if it also counts for planetary defense fighters.
d ) Overall, I think the upkeep for ships is a little too high and, the AI still spawns them like there is no tomorrow. I get that the AI may need a boost here and there, but it should also pay the normal upkeep.
e ) The AI should build their planets in a more optimized way. When I conquer a planet, it looks in most cases like a mess. It should at least try to build similar buildings beside each other to get bonus points and also re-arrange buildings once the tech advances to maybe have a different layout.
f ) It might be nice to have the ability to place your colony-hub (the first thing you get) by yourself or at least be able to "relocate" it.
g ) PLEASE add a planetary editor to the map editor, so that I can also edit the planets. This is a feature missing for the long term unlimited play style I love to use.
Thats about it. Hope it helps!
Cheers!