First of all I want to say that I absolutely loved the GalCivII, but here are some things I have noticed in this beta.
Now it's been awhile since I last played so I forgot a lot of stuff, THERES NO TUTORIAL!!!! So basically I have to try to remember how to play, I'm not sure how new people will learn how to play but there really needs to be a tutorial.
Also almost every time there was a loading screen it took about 3 mi
Still in Beta (Beta 4 patch 2) this will be in the final release of the game set to happen in May of this year. (as stated by Franco FX & markmid)
Also almost every time there was a loading screen it took about 3 minutes, it may not sound like a lot but it is a long loading screen and there is no way to tell if it is frozen or not.
Game is not fully optimized at this point, plus will have to do with your system specifications. Slower computers will have longer load times although seems a little much.
Then when I went to pick which empire I wanted, the benefits and what not when I hovered over them some didn't fit in the little description box, the formatting was off, this also happened when I hovered over the different buildings I could build on my planets.
Text cropping is a posted bug and they are working to correct this.
Since I have two monitors side by side, while the game is running I can move my mouse over to the right and my cursor goes onto my other monitor, this doesn't happen with other games that I play and it is very annoying.
Personally I don't see this issue as a bug, I love the ability to continue working on something on my second monitor while in game and bounce between the two. This comes into play especially during a multiplayer game where you are waiting between turns I can just jump over to the second monitor work on something then bounce back. Being that Galactic Civilization III does this for me I hate now that I can't do this on other games that I play. Don't take this away keep it and I wish other games also did this. 
Also there should be a mouse scroll, like put your cursor to the top of the screen and the screen will move instead of using the arrow keys every time. It would be much smoother with a mouse scroll.
Edge scrolling would be nice and has been mentioned several times... I hope it makes it into the game soon.
And the game freezes.
Posted on many bug reports. Stardock is working to correct.
