1: Better UI. Civilization IV should be the minimum standard.
2: Combat should not be random. This is a personal pet-peeve I have with all TBS games.
3: Combat should not be reduced to simple "bigger number == win" type of things. Or at least, not always. Ship construction should feed into that; a fleet composed of the right ships with the right abilities should be able to defeat other fleets that are bigger/have bigger numbers/etc. Ditch the 3 attack vs. 3 defense nonsense in favor of something else.
4: Ditch the resource model entirely. Design a new resourcing model from the ground up that uses equations that are:
4a: Visible to the user.
4b: Don't require higher than a 5th grade education to use.
5: Trade needs to work better. A smaller nation should be able to specialize in "trade" (not the GC2-style of trade that just creates money for both sides) to the point where they can get another large nation dependent on trade with them.
6: Ditch StarBases. Replace them with something that isn't a chore to build.
7: Random galaxy generators need to be programmed to make sure that every side has some decent territory. Alternatively, expose (preferably via Lua script) the ability to allow users to add galaxy generator scripts, which should be able to do this themselves. They should also be able to expose UI elements for properties.
8: Planetary Invasions should remain relatively simple (in the sense that we should not have to build different types of ground troops, etc). However, it is not good that a space fleet is entirely useless to invasion. Ships should have modules that aid in planetary invasion (balanced by the fact that such ships are weaker in regular combat, since those modules won't be attack modules). Planets should be able to build defensive buildings that don't consume precious tiles. Tiles are a vital resource, and you cannot justify consuming them just for defensive purposes. You should be able to build a "fortress world" that is neigh-untakable without the enemy investing heavily in it. But at the same time, there should be a strong cost associated with bunkering a world so heavily. Just not a tile-based cost.
9: Develop a combat/ship construction system that encourages dual fleet building. That is, having defensive ships and offensive ships, and having these two kinds of ships be separate ships. In GC2, the same fleet you use to attack will also be used to defend. That is not as it should be.
10: Obey the Law of Small Numbers/Law of the d20. That is, a +1 bonus should always be significant. A +3 bonus should be substantial, and a +5 bonus should be monsterous. Anything that gives a bonus should give a significant bonus. That means that things like anomalies that give out lots of little bonuses have to go away. Giving out fewer, but more significant, bonuses is better.
11: Never use decimals. 5th grade math, remember?
12: Ditch the Twilight of the Arnor-style tech trees. Instead, have fewer tech trees (more races share the same tree), but have more distinct trees. As in, have some trees that are more like Civilization-style trees (lots of requirements and inter-dependencies), while other trees are more GC2-ish (more focused, but more techs overall). Best-case would be 3 well-balanced trees. Separate tech tress should have no techs in common; two races that use different trees have fundamentally incompatible technologies.
13: Game-changing techs. Gunpowdered in Civilization changed everything. If you didn't have gunpowder, you were fundamentally behind the times, and likely to get steamrolled. Same goes with Internal Combustion. Have certain techs that dramatically alter the balance of power, such that researching them quickly can be a viable strategy (the cost for doing so being that you're weaker in other areas). Something for GalCiv would be like the ability to create wormholes, allowing your fleets to jump to various locations, thus reducing your dependence on your ships' hyperspace movement speed. These should be tech-tree specific.
14: Ditch the espionage system. Replace it with something that doesn't suck.
15: Develop a planet quality system that ensures that every planet is viable. This isn't Civilization, where terrain is everywhere; if a planet is colonizable, it should be something that you can actually use. That is, there are no bad planets, merely planets that you can't colonize yet.
16: All planets should eventually be colonizable.
17: Follow the Civilization IV design mantra: reward instead of punishing.
18: Either remove government systems entirely or make it more interesting than just a bonus for researching certain techs.
19: Ditch the UP. Instead, institute a more generic system, where various factions can set up unions among themselves.
20: Tech trading. Allow the ability to trade the fruits of a tech instead of just the tech itself. This allows you to choose to prevent the other guy from whoring out tech. Of course, whoring is lucrative, so trading the fruits alone is not as valuable as the tech itself. Also, they can't build on fruits alone. Tech trading is only possible between races that use the same tech tree. For inter-tree trading, researching certain techs allows you the ability to trade special things that are not found on the other guy's tree. You can't use them yourself, but it allows them to gain some of the flavor of your tree.
21: Each of the tech trees should have a unique superweapon. These superweapons should all work differently (one can work like Terror Stars, but the others shouldn't).
22: No tactical battles.
23: Ditch the gampaign. Instead, integrate the game's storyline into the gameplay. Look at Alpha Centauri and how they integrated that plot into the normal game.
24: Ditch asteroids. There should be colonizable asteroids, but those should functionally act as regular colonies.
25: Revamp the event system. Events should not take place instantly. The Dread Lords event is really the ideal; it happens, and you need to deal with it, but not necessarily right now. AI needs to be better able to deal with events.
26: Ditch influence. Replace it with a better alternative-planet-capture mechanism that isn't dependent on being able to militarily protect StarBases while the computer rolls dice to see if a planet flips.
27: Ditch diplomacy. The stat, not the concept. Replace it with nothing, as gaming the AI is a fundamentally bad idea.
28: Ditch surrender. Instead, allow civilizations to become vassal states. These are states that are supposed to do what you tell them to do. You tell them how much trade they must do with you (and where to do it, if location matters). If they fail to fulfill their obligations, they lose their vassal status and become enemies again. This allows lots of cool things, like the Drengin becoming vassals as a temporary measure to rebuild their army. If you don't "tax" them enough to keep their army small, they'll grow strong again, and possibly overthrow your rule.
29: Ditch fighters entirely. Any ships you build should be of "corvette" size or bigger. "Carriers" would just be ships with special carrier modules that spawn a "Fighter Fleet" ship at the beginning of combat. Even if the ship is destroyed in one battle, it is considered reconstituted in another (just as ships don't run out of missiles).
30: Ditch range. Replace it with nothing. It was a bad idea.
31: Avoid techs that are "What you had before, only with a +1 bonus." Instead, develop a resource model that allows later "manufacturing" techs to improve manufacturing in different ways. Not just a better building that does the same thing only slightly more.
32: Ditch morale and population entirely. Replace them with nothing. That certainly has the virtue of never having been tried.
Um, FYI: in space, there's no "ambient" light.