LOVE:
Hex maps
The music
The 4 subsidies at the bottom of the planet project list
The sidebar interface showing research project progress, etc. The single-digit date is weird though.
Like:
Adjacent hex bonuses for buildings
Not Crazy About:
Where the game puts the Colony Capital. Half the time it puts it in a hex way off by itself, depriving me of any adjacency bonuses
What would be AWESOME is if *I* could decide which tile the colony capital was going to land on!
Still only a max of 5 planets per system? 
Multiple bonus tiles, such as +2 manufacturing combined with +2 population or +2 influence improvements. Why?
Planetary and Empire production adjustment wheel - sliders were simpler; useability is the goal, not stupid/sexy, right?
Yellow ocean hex on Earth lists as Arid Land - what?
I had +10 Benevolence and +30 Malevolence, but the Ideology window wouldn't let me move to the Malevolence tree so I could unlock my first block. Of course, the "Ideology" button wouldn't go away so I couldn't hit next turn, meaning the game was STUCK AGAIN and I had to trash it to restart. If I don't want to spend my ideology points right this very frickin' second, the game shouldn't make me do it.
Bring back the robot reporter who listed everything that was built/happened at the beginning of each turn.
HATE HATE HATE:
The Eject Ship button
How the planet tile icons all mean something different now - Why do you hate us? Either CHANGE to DIFFERENT icons, or make them match the GalCiv2 icons that WE'RE ALL ALREADY USED TO!
Homeworld Civ Capital and other Colony sets up on bonus tiles instead of normal tiles. Example: Homeworld capital was sitting on a +2 Manufacturing. I could've built a factory there, but Nooooooooooo...
Idle Ship - notification is nice, but doing something about it should NOT be mandatory! "Pass" should just be assumed if you don't move the ship after being notified, and the game should just notify you of the next idle ship. If I have to hit "Pass" for every ship I don't want to move in a huge galaxy I might just get in my car and drive to where you are and... well, nevermind. Just fix it.
I had a situation where my survey ship found a lost cutter so the 2 ships were stacked. The cutter was idle but the game wouldn't let me click on it
to move it or pass. They weren't in a fleet so I couldn't "eject" one ship out. Spacebar didn't work to "Pass" either. I had to trash the game and restart. Stupidity run amok.