At the beginning (Turn 1), after the galaxy is generated, it would be nice to have a "regenerate map" feature much like what Civ5 has. The reason is that I like to have a game where my starting planet is roughly in the centre of the map. This provides more opportunities for challenge and fun when dealing with other empires. This would save me the headache of constantly going back to the main menu to reset the game.
They keep saying this is eventually coming, I believe the latest news was patch 1.4 also known as (ctrl+n).
I think there are difficulties with the AI. For one, I found that an empire just doesn't know when they're getting their asses hand to them. In the diplomacy screen, it indicated "you are weak" to the enemy empire, but I was anything but. I just treated them as a nuisance. Occasionally they'd send a fleet across my border and I'd quickly blast it to pieces without incurring any losses. Occasionally I'd send a fleet in their territory to "teach them a lesson" and I'd blow up any fleet or starbase I'd find (again with no losses to myself). They'd still stubbornly persist in a war against me when I tried to negotiate peace.
I found this the opposite, I couldn't force an AI to declare war on me I was too powerful, none of them wanted to mess with me even though I was running away with the game.
And odd thing I noticed was when I eventually got to the Age of Ascension part of the game, my research capacity completely left other empires in the dust by a ridiculously huge margin. The gap just grew and grew and grew, and the other empires' research levels were just stagnant for the remainder of the game. The difficulty level was normal, so I'm puzzled how I could have completely dominated the technology race.
Four reasons. First it depends on the AI's focus on technology for that specific faction, if it's low on priority they seem slow. Second if you have tech trading on this will also leave the AI in the dust as they don't take advantage or very poor advantage of trading techs to other races so the player can get their hands on many more techs much more quickly than the AI knows how to do. Third the AI has to build research buildings next to each other to take advantage of the adjacency bonus's and I find that they are poor on doing this as well. Fourth the AI is poor on placing economy star bases near planets and therefore can't receive the extra production/research/economic boost they provide. This will allow the player to have planets producing over 1000 points per turn in any of those categories while the AI may have 100.
I think this was discussed, but it would be nice to have at least some animations involved in ground invasion, just to see how the troops perform. I think something simple like the Master of Orion II ground invasion animations would be a useful model for this.
Is eventually coming I thought it was patch 1.3, however, much of this has moved around so many times it's not funny. This should have been in upon release, however, do to time restrictions (even though it could have been adjusted easily enough as everything is digital and they made it a point to note this several times during production) they pushed it to a free post release patch. I'm hoping by patch 1.4 they get most of the annoying bugs and quirks cleaned up. 
Stardock is normally very good about player feedback and correcting things.
To make the game more exciting, I think some mega-events would be nice to make things interesting. Rebellions/revolutions, space monsters, viral outbreaks, powerful invading aliens from outside the galaxy, or whatever. In a previous post, I suggested some ideas for near end-game apocalyptic mega-events.
Mega events were left out of the base game because of the ideology bonus's. They originally felt ideology would offset some of these events. I feel this has taken away some of the game twists especially middle to late game. I hope these are brought back in an expansion.
Some of the ones I miss....
Random minor race found.\
Planets break away make a new faction (although annoying helped to stretch the game for those that love that type of thing.)
(Dread Lords) An all powerful race enters the game with a fully built up class 26 (or more) planet ready to conquer the galaxy.
All planets double in planet class around certain object and extends out so far.
All planet qualities increase by x around certain object and extends out so far (even class 0 or dead worlds)
Planet is destroyed by comet.
Ones I don't miss.
Random pirates are generated throughout the galaxy (In Galactic Civilizations 2 this meant the galaxy was now filled with pointless fluff that you had to clean up or be annoyed by.)
