Some great suggestions here, but some that I think would be hard to do because anything you add for player fun has to be usable by the AI within reason - and sometimes people suggest things that seem simple on the surface, but that would be a nightmare blend in for AI use.
Of supreme importance:
1. Fix bugs. A given, you'd hope, but it always worries me when discussions of new stuff occur and there are bugs that haven't been fixed for several iterations.
2. AI enhancements/adjustments. I'm sure they'll happen, they always do, and they help keep the game fresh.
3. Fix tech trading - it has never felt right, IMO. Needs to be fair for both player to AI and AI to AI trading (including majors and minors). I liked someone else's idea of a yearly limit on number of tech tradeable, based on another tech tree line, or empir size - something (you could say on diplo, but diplo is so highly cheesable in this game already). You have to limit trade routes to "keep it real" - the same type of limiting needs to occur on tech trading. You could even add more UP decrees to artificially limit as it does with trade and other stuff.
4. Fix war declaration. War can be harsh - it ruins trade, leads to bad relations, slows down empire development, etc, and it's often insanely cheap and easy to get someone to go to war. Conversely you often have no option to get someone to go to war at any price, which is equally ridiculous when you consider the magnitude and radically game altering potential of a large number of random events in the game. You should be able to get someone to backstab their ally if you pay them an exhorbitant amount (100,000+bc, 10+ juicy techs, a few planets - dunno what a suitable bribe would be, but it shouldn't be a non-option).
5. Some elements don't seem to scale well with galaxy size. Perhaps "buying wars" is one of them. 2-3000bc on a smallish map might be a nice chunk of change, but on large and up it's chump change.
Realistic changes (things that wouldn't cause AI seizures):
1. UI changes, like better sorting/display options on the planet screen for structures. Sometimes it might be nice to see only factory type structures, or lump factory and powerplant as "production" structures - some kind of breakdown of types in order of potency, with clear indications of potency. A lot of times when developing worlds in late game I'll build lower level variants of structures and upgrade them in cycles, so they develop in my lifetime - and it's tedious to have to do this manually as it is - moreso when you have to sift thru the multitudes of structures to find what you want.
2. UI changes, like better sorting for ship components when building ships. If I pick weapons/defenses of a particular type, I want them to sorted in a particular order, and the game seems to do something way different than that. I want them in order of damage/defense value (highest to lowest), then size (lowest to highest), then cost. Sometimes it seems to do this, sometimes it does not. Different sort options or consistency would be nice. The likelihood of ever wanting to sort weapons/defenses/engines by alpha is slim.
3. Oddly, I mostly played with missles til recently, when I forced myself to try beams, then mass drivers. The nano rippers were a nice surprise and so different from the usual generic progression. More variance in the fairly linear tech trees (like nano rippers) would be nice, especially in the weapons/defense/engine lines that make up the effectiveness of your ships.
4. Often I have fleets of the exact same ships - maybe it's 5 mediums - exact same design. If there's a way to upgrade all at once, I've missed it. It'd be nice if you could upgrade a whole fleet at once (assuming they can all upgrade to the same ship and you can afford it). If you have a booming econ and can afford sweeping upgrades, it can get real tedious to manually upgrade ships 1 at a time. Maybe even adding a ship upgrade governor could be an option (although, it probably wouldn't see much use since it's rare that you can just flat out upgrade your entire navy at once).
Ideas that the AI would probably have problems with.
1. It would be cool if you could use production to upgrade ships instead of cash. There are several ways you could do this.
a. Mining bases on asteroids could assign production to a nearby (very close) ship which would feed the upgrade. It would require a special module on the mining base. In most cases, you'd probably need a whole field decked out to assign for the upgrade. Probably my least workable suggestion.
b. A ship adjacent to a planet could be upgraded with that planet's military production. Perhpas the planet would need to have a star port AND an additional structure, like a "star drydock." There could still be a small upgrade fee, but the bulk of the upgrade would use planet production. The upgrade time would depend on the output of the planet - so you'd likely have to do it at your ship building worlds. (my favorite suggestion for this)
c. A ship adjacent to a military starbase could get reduced upgrade costs. Make a line of modules for military starbases that reduce upgrade costs by 5% per level. Make it so that you can't add these modules til the military starbase already has a certain number or type of existing modules, or til you hit a certain ship tech level (could add it in with one of the less impactful ship techs - one of the ones that doesn't add new hull sizes or hp bonus). This would make military starbases more useful!
d. Either use constructors, or make a new type of module that can be used to help with, or enact ship upgrades (ties back to planetary production doing upgrades). Merge these with a ship that's upgrading to reduce/defray/refund upgrade costs or do an entire upgrade if the "production value" of the constructor is high enough. If you used a new ship module type, you could theoretically have cargo hulls with varying amounts of these modules to various sized upgrades, and it would probably require multiple such ships to fully upgrade medium or higher ships. You could even have a whole new tech line (or suppliment an existing line) with more and more potent "ship upgrade" modules.
I think the AI would have problems with this whole concept because no matter how you do it, it's more complicated than simply upgrading with cash, and if the AI has to pick between cash and an alternate method, amongst all it's other decisions about what to do with cash or production, then it becomes enough of a programming hassle (requires AI coding and new interfaces/core code for the physical mechanics) that a dev just says, "nah, I'd rather do a simple UI upgrade" (I'm a programmer, I know these things
And this is what I was aluding to at the start about implimenting some of the ideas players have.).