I recently finished a gigantic game, during which I wrote down all the bugs that I could find.
Here they are:
Planetary Defense Bug - The planetary defense bonus from one of the colonisation events doesn't show up under Planet Bonuses in Planet Details.
Research Complete Screen - There are lots of missing info on this screen: New Ship Components, New Starbase Modules, New Invasion Tactics.
Same thing when right-clicking on a technology in the Research- or Trade-screens. New Ship Components, New Starbase Modules and New Invasion Tactics aren't shown.
Minor Race AI - Andians declared war on me, saying that I had parked transports around their world. I hadn't even found their planet at the time. All I saw of them was 2 scouts and they had no way of seing any of my transports.
Turns left for production is still incorrect in the Colony Management. The correct one can be found in the Civilization Management.
There were two times (that I noticed) where I didn't get a GNN notification when a two AIs began fighting. First when Korx and Torian went to war with each other and the second time it was Drengin and Torian.
Andians and Snathi use logos from Galciv 1 which are of much lower quality compared to all other logos. They are racelogo21.png and racelogo22.png.
Ships can still have more then max hp after repairs. Noticable if a ship is being repaired on a planet.
On some planets, demolishing or replacing an Orbital Fleet Manager or a Starport makes it impossible to build again. I have no idea what causes this, on some planets it can be rebuilt, on some it can't. Very annoying.
When the map is maximally zoomed out, ships can wrongly get a attack-ship icon instead of a defense-ship icon upon exiting a planet. This happens when the ship has more defense then attack but the attack bonus on the planet makes the game think that it currently has more attack then defense. This means that it will get the wrong icon but once you begin to move it, it will change to a correct defense-ship icon.
Upgrading a ship in the fleet manager exits you from it. Annoying if you want to upgrade multiple ships.
Quarterly Report bug:

Drengin AI had the alignment event where it reads that they have become good. They didn't though, probably because they already had Xeno Ethics and their alignment was locked to being evil.
When reloading a game and looking at the timeline in the Civilization Manager, it will read "past 0 weeks" even though it is showing all weeks.
Improvement Summary bug. Morale and Influence bonus shows incorrectly after improvements have been built on their bonus-tiles:

AIs build very bad constructors late in the game. Drengin Constructor M5-9 has 5 ion drives. I know that he had Warpdrive Mk.III on his M5-5 warships. Arceans constructor M5-11 also had 5 ion drives.
Korx also built a sucky transport late in the game, their M6-3 had 4 ion drives. I know that he had Hyperwarp at that moment.
When a constructor fleet constructs a starbase, the fleet disbands on the starbase square instead of further upgrading it.
A constructor fleet also disbands as soon as they begin upgrading a starbase. For example, I have a fleet of 10 constructors and upgrade 3 modules on the starbase. Now I must reform the remaining 7 constructors into a fleet again.
When a planet has suffered damage during invasion, a popup appears after entering and exiting the planet saying the number of planetary improvements that has been destroyed. Wouldn't it make more sense if it pop-uped before entering the planet? I think so.
It would also be nice if it actually said what kind of buildings and how many of each type that had been destroyed.
When starting the invasion combat, a red X replaces the building or buildings that got destroyed from damage. It would be much better if the red X appeared on top of the building so that it was still possible to see which kind of building was destroyed.
Not necessarily a bug but when a race surrenders because of the player it isn't counted in the victory tab in the Civilization Manager even if the race surrenders to, or, because of the player. I was the cause of the destruction of all 9 major races and 4 minor ones but according to the CM, I had only destroyed 6 since I didn't do blixtkriegs on everyone and conquered all their last planets in one turn.
After the last AI was dead, I could still see him in Foreign Policy on that same turn.
In the End Game Summary - Most Powerful Ship includes both fleets and starbases. It would make more sense if it only included ships in it's calculations.
Typos:
All the 3 evil weapons-technologies has names that begin with Psionic. It also says psionic in the description. All 3 evil weapons have names that begin with Psyonic.
Technology Superior Hulls description "This gateway technology gives us the knowledge on how to be very very large hulls."
"be" should be "build".