I'm going to start out by saying I think this game has enourmous potential. It reminds me of one of my old favorites, still on the hard drive, Conquest: Frontier Wars.
I'm running on an AMD Athlon 64 X2 Dual Core, 2MB Ram, Vista Ultimate 32-bit, nVidia 7950GT cards running the latest beta driver (101.41) and operating in SLI mode.
0.61[b].009 is crashing on me a lot more frequently than older builds. I've yet to have it let me finish my first fight over a rock against pirate scourge so forgive me if some of this has been addressed, I just haven't seen it yet.
Comments and Suggestions
As the game currently stands it's already pretty fun, skimming the forum there are some suggestions to improve things. The phase jump stuff is reminding me of the Honor Harrington books by David Weber where you have to go so far out from the gravity well of a planet and/or star to go FTL. Some suggestions have it going out farther and introducing beacons and so forth, I think that would be cool. Perhaps even set the gravity well size as an optional component. The idea of having spying outside the well and more strategic options I find compelling.
So far my biggest problem with the game is dealing with fleet operations, I realize not everything is 'in' yet but the ability to create fleets and give orders gets a little on the tedius side. Perhaps put in something for general fleet orders like 'sweep system' 'guard position' 'assault' 'cripple' (perhaps target only structures or trade) 'raze'. I would also like the option to have fleets/ships not attack certain stuff, I'd really rather them not attack trade ships when there's an enemy battleship next to it. While we're at it options like 'go back to homeworld' or 'retreat and find repair station' might be good too but that's probably getting into a programming nightmare.
The AI seems to create and break treaties very randomly; treaties should be harder to break perhaps. Maybe certain alliances (cease fires) would have a time period of 'neutrality' before going back to hostile. The AI at least seems to use cease fire agreements to scout out your system and position forces and then break it when ready.

I like the 'announcements' when stuff is arriving etc but it would be nice to have trade/mining ships and other small fry that I can't control anyway be excluded (perhaps as an option).
Anyway just some thoughts.