If you build a unique player structure like Hyperion Logistic/Hyperion Shrinker/Tech Capital/Manufacturing Capital/Gaea Vortex etc., on a world, and then lose that world, you can build the same structure on another world. When you retake the lost world you then have 2 copies of a unique structure. Cool, huh? No, it completely breaks the game. You can have ships with tens of thousands capacity, you can have dozens of structures that provide flat bonuses to your entire empire. The best way to abuse this is to trade a world to an AI that you've build all your unique structures on, wait until you've rebuilt them all on another planet, and then retake the old world. Then, trade both those two world to another AI, build all the unique structures on a third world, and retake the first two. Rinse and repeat.
This is far and away the strongest way to play and is extremely unfun to do. Stardock, you need to make the program check to see if a unique structure built by a race still exists in the galaxy and not let the player build another if it does. Just checking to see whether I currently control one such structure won't work.
Another related point is that the only way to get many ideologies is to take the Zealot perk and abuse it in similar fashion. You trade all your worlds to an AI and retake them, then trade them all to another AI and retake them, and repeat. This is profoundly unfun.
You might say that the player just shouldn't do this if it isn't fun, but understand that for min/max players just having the option available ruins the game. We must pursue the best strategy, playing the best strategy is what we find fun. When you make the best strategy unfun you ruin the game.
What you need to change to save the game:
1) Make the program check for unique structures as I've described.
2) Introduce another way to get and farm ideology points; let the player actually build or buy them. The current structures that give them per turn don't give nearly enough, by the time the game is ending you're lucky if you've unlocked one line of one branch. Maybe you could let the player spend credits to create public works projects that give Benevolent or Pragmatic points, maybe sponser pirates to get Manevolent points. Maybe just let the player build the points directly the same way you can build culture/population/credits.
3) Games are waaaaay too short. Even on huge maps it only takes about 150 turns to get every tech and build a fleet of doom. Make technologies dramatically more expensive, like 3x more expensive. Then there would be more focus on securing resources and fighting for planets.
4) MOST IMPORTANT: there is a game breaking exploit, even worse than cheesing unique structures and ideology: the game let's you trade weekly payments for literally everything an AI has at any point in the game. You can, for example, rush Universal Translator, contact an AI, and offer them 600BC/week for all their tech/ships/worlds. Then you declare war on them, this cancels your obligation. They don't even hold this against you, provided you didn't offer any enduring treaties or other resources. I can't resist doing this, it breaks the game. Please make it so the AI doesn't accept weekly payments from the player. You could try just limiting the amount of weekly credits the AI will trade for to some scalar of the player's economy, but nuking this feature is the only way to be sure. This has been broken since forever, please fix!