Okay, I'll bite:

1. I wish starbases, or a certain type of starbase, could be built in orbit around a planet. Even if it's just a basic weapons platform, the lack of any planetary defenses other than regular ships causes me to frown.

2. I wish minor races would offer things above and beyond what your regular races could/would do. Give each minor race a mid-game tech only available only either through espionage, trade, or capturing their home planet.

3. I wish other races would place priorities on the techs they want, either to complete a particular ship design they want, or to fill a hole they need. I'd love to have to contact the military race to sell planet improvements to fill in their holes, while peace-loving civs will buy defenses and armor at a premium.

- When you destroy your own star base, some "resources" are "beamed" to the nearest planet, like an asteroid field, to account for salvaging a little bit of the resources used to create the star base.

- I wish minor races were harder to manipulate for tech, money, wars, and wish they had a +50 defensive soldiering bonus to make them slightly less easy fodder once everyone gets their military rolling (and usually take out nearby minors for easily obtained uber worlds).

- I wish tech trading could be done so that it was within reason and not exploitable by players or amongst AIs.

Realistically the only thing I'm concerned with is tech trading, which has always been a problem in GC, as far as I'm concerned. It's never been balanced well.

It's cake to pump out tons of constructors (if you want to) and you can always limit yourself to intelligently placed and useful starbases, with the occasional purposeful military or influence base that you get good use out of and therefore don't need something back if you destroy it later - that's just greed. For example, a well placed influence base might flip one or more planets for you. Wanting to get something out of destroying it after it's no longer needed is kinda greedy when it got you a planet.

Minor races can benefit the player or the AIs - a lot of it depends on luck, and they can be disabled if you find them annoying/unbalanced. I don't think diplomacy with minors needs to be that robust - the minors are fodder - they're there to add flavor, not be serious factors in diplomacy. Why would you want to subjugate them diplomatically when easily taking the world via military is vastly more beneficial? Why put a minor world symbolically under your protection when you can easily take the world, develop and use it how you want, and protect it as part of your empire. Not all players want to win via military, true, but you pretty much have to develop military to not get wiped even if you go for a peaceful victory, and you're going to have to have enough military to threaten a minor to make them join you, so you might as well just take them out - it'd be way simpler. More diplo options amongst majors would be dev time better spent.

1. I wish starbases built on galactic resources had influence points of their own so a player would be able to win them over culturally, even if it required a lot of influence in the area to do so.

2. I wish minor races would recognise the closest powerful empire to them and pay tribute to the said empire for protection if the said empire is good, increase tourism income if the said empire is neutral, and lastly, increase production if said empire is evil.

3. I wish there was a slider for tech trading controlling how willing AIs are to trade techs.

1. Guardians for anomalies. I'm not sure whether this is possible, but it would be nice if you had to fight a sort of guardian (a la MOO) before exploring some anomalies, that automaticaly appeared in the sector. The guardian should be quite powerful (old Dread Lord sentinel,Arnorian Protector, Space Monster, whatever), but the reward should also be worthwhile (instant tech, a bundle of resources, a large plus in some ability, A powerful ship or relic, etc.). That might keep some anomalies unexplored until mid- or even late-game, and keep you on your toes- perhaps even more than the late grabbing of planets with new colony tech.

2. Sublugation and Protectorate! I totally stole that from the diplomacy concepts from ol' Space Empires 4. It might be unbalancing as a standard diplomacy option, but it would work well for relations with minor races, I think.
In Sublugation, A minor race agrees to be a thrall to the larger one, paying tribute from taxes, sharing tech, even offering ships and starbases.
In Protectorate, your grasp on the minor race is less firm; but you still get techs and trade in very favorable terms, gifts are more common and requests are much more likely to be accepted, and the race is a faithful ally "willing" to go into any war with you (and suffer the blows for you).
The downside could be that both treaties would not improve your relations with the races any more (sublugation might even worsen it, if only slowly). So, If you don't protect your sla.. your protegees enough, or you are too bossy and demanding as an overl... a "protector", they may decide to break loose from the treaty themselves, and even be hostile to you afterwards.

3. I got nothing.

1 I would like anomalies to randomly generate throughout the game so my survey ship doesn't end up becoming a glorified scout ship later on. Have less of them at the intial start of the game then have them appear here and there over time. And I like the idea of having some quests attached to some of them.

2 I would like minor races to have personalities that are more unique and in keeping with their role in the game. For instance, they should have no interest in trading any of the colonization techs, nor should they be building Influence Starbases that do absolutely nothing. Have them build Military bases near their planets instead, as well as more/better ships. It would make them more of a challenge when it comes time to conquer them. As it stands, they behave exactly like the major races do, even though their focus is completely different.

3 Races shouldn't be able to trade/steal/conquer techs that they don't already have the prerequisite techs for. No going for Lasers unless they already have Beam Theory. These more advanced techs shouldn't even come up in the trade screens. I think this would go a long way to fix the broken tech trading situation we now have. There wouldn't be as much of a need to go to the drastic measures this last patch has gone to in order to control it.