Graphics:
I want many (if not all) ships to lose size in relation to capital ships, namely cruisers.
A bit of maneuvering during combat would be nice.
Ships should not become bright gray when you zoom out in cinematic mode.
Cinematic mode should make distant planets appear as dots for the sake of screenshots.
Planets should be slightly bigger.
Combat:
This is the main catagory that needs improvement, in my opinion.
More combat ship types. Currently there are loads of support ships, but only three main types of combat ships: heavy cruisers, long range frigates, and combat frigates. I would like to see an entirely new ship type, destroyers, that focuses mainly on combat. This would allow effective counters to support cruisers, etc.
More interesting combat abilities. I'd like to see counter measures against missiles, directional shields that shift to face whichever side damage is heaviest on, giving flanking attacks an added bonus, ships that can truly make use of a longer range by autonomously maneuvering well in combat, anti-strikecraft weapons on capital ships (honestly, why isn't this in already, and anything else to make the combat more deep. I don't want an ability microfest (like a blizzard RTS, grrrrrr), but I do want movement and fleet build to be important. Fleet positioning within the gravity well should play a huge part in the outcome.
Information warfare. As is, it's nonexistant.
Empire Building:
More in-depth empire strategies, government type would be nice. It would also be nice if every single thing that benefits your empire wasn't orbital, being able to develop things on the planets surface could be nice. Overall, however, I think the empire building in SoaSE is solid as it is.