A few ideas that came into my mind while playing the Beta. Some of them might have been mentioned before. If so, I am sorry. 
1.
I kind of dislike the constructor spam caused by the fact that your constructor vanishes each time you are using it. Why not doing it the way Civ Beyond Earth is doing it with the explorers and their explorer modules? You build a constructor with one or more construction modules. You move your constructor, build your starbase or an upgrade and the module is lost BUT the constructor isn't. Now you move your constructor back to the shipyard where you can reload its construction module in exchange for money or just by waiting one or two rounds.
2.
I would like being able to break UP resolutions. Example: the resolution which prohibits colonizing new planets passes in the UP. Now you are having two options: 1. Comply. 2. Not giving a damn about the UP and colonize a new planet anyway. If you do that, the UP will hold a meeting immediately discussing how to deal with you: Imposing a fine on you, imposing an embargo on you, declaring war on you... That would make the UP and diplomacy even more exciting in my opinion
3.
Habitable starbases. I don't know if this would break the game but it could compensate for a bad starting position. You build a starbase with a constructor and add a habitat module to it. That will turn the starbase into an artificial planet (like the Citadel in Mass Effect ). This starbase acts like a small planet (2,3,4 tiles) just without any bonuses. So you can build factories on it or any other building you could also build on a planet. With advanced technology and constructors additional tiles can be added to these starebases. Of course they should never be as powerful as a real planet.
What do you guys think?