I am running Beta 4 with Opt In Selected on Win7 x64.
All of my drivers are updated.
I have started over half a dozen games so far and I was unable to get far in any of them.
Either the game goes into a forever waiting state while it is the computers turn or I ended up quitting after all of my planets are taken over by Influence.
It is usually a race to see which one happens first.
In each of these games I played as Human and created a Huge galaxy. I tried to change as little as possible when attempting to isolate the issues.
I tried to create a support ticket and upload a saved game but I got an error while uploading the file and gave up and went and made dinner.