I've only played about five hours by now and, so far, I'm pretty impressed. The Alpha is much better than I expected. It's obvious, that there is still a lot of work to be done, but the start is already very promising.
During the five hours I had one CTD. According to the debug.err a crash report was send to Steam, but I can upload the crash.dmp, should it be needed.
Okay, here are some thoughts about the game:
1. Options:
A. 
Overall, I'm really happy so see this menu. As far as I know, it's the first time, that you can change hotkeys in a Stardock-game.
2. Choose Civilizations:
A. 
3. Colony Management:
A. 
B. 
C. 
D. 
E. The buildtime of improvements and ships isn't updating immediately when I'm adjusting the Total Manufacturing value.
4. Starbases:
A. 
B. When a constructor reaches the starbase, I'm not getting a prompt to add a new module (if I have one available). Due to this, I have lost several turns, because I didn't notice that the constructor had arrived.
5. Main map:
A. 
B. 
C. (Picture removed, because the Shielded Planet bonus got fixed in 0.0.2.0)
D. 
7. Minimap
A. 
6. Tech Tree:
A. 
B. 
C. 
The same is happening with several other techs too.
D. 
E. 
F. (Picture removed, because the tooltip for Tech Specializations got fixed in 0.0.2.0)
That's it so far. I'm going to update this list, if I find anything that hasn't been reported yet by others.
The biggest item on my wishlist at the moment is an End Turn Summary, like the GNN in the previous games. Primarily because I have far too often missed that my ships have been constructed.
Edit: Added the zip-file with the crash.dmp as external link, just in case.