First one is, I absolutely love the Alpha. It's decidedly playable & stable, so mega kudos to Stardock for it A couple of things that I've noticed / improvements that can be made.....

• When you run out of tech on the tech tree you're no longer able to complete a turn. I got to the end of the tree just to see all of the things that I could build & then sat there for about a minute ending the turn over and over again and wondering why nothing moved or constructed.
• The specializations on Tech are cool - but I think they can be improved. When you research a specialization you should be able to select the bonus that it delivers - ie, if your specialization improves missile drive systems, you should get a choice of if that manifests itself as increased payload (extra damage), increased missile speed (harder to counter) or increased range (better stand off capability) for example. That'd mean the specializations would have some weight and customisation and allow for a wider range of play styles & battle tactics.
• Really minor one, but after you capture a civilization capital the note on the galaxy map that it is one remains. My personal preference would be for some kind of "Occupied" Notification that tells you / anyone else that you didn't originally colonise the planet. There could also be some interesting bonuses for occupied planets - perhaps with choices post invasion.
• Also, there seems to be a big around combat. Often when large fleets of AI ships are orbiting planets, my own ships are unable to engage them - which since they don't move, has at least once lead to a planet being impregnable, because there's so many ships orbiting it!

Anyhow. Those be my thoughts. Phenomenal game so far - really looking forward to the next phase!