I've run into a bug where press the "turn" button and then I have to wait forever. I can select any of my units, so the game clearly doesn't freeze, but seems to wonder what it should do (Let me continue of course!)

I've run into this bug twice. The first time, I was able to circumvent it by saving the game (which I can while waiting, saved as "Game1"), then reloading. When I reloaded, I immediately got the animation of a flagship being launched (not sure what my flagship was though, I couldn't see it anywhere being marked, maybe I looked in the wrong part of the screen).

The second time, I decided to do the same thing (saved as "Game2"), but it didn't have any effect. Reloading Game2 got me in that second neverending "wait" session and reloading Game1 got me to do the turn and then get to that second neverending "wait" session.

---And I finally had a nice region with good planets (rather than only dead ones). That's not the primary point of course, because this is a beta.