Well, my work schedule didn't allow me to jump in when the Beta was first released, so I'll avoid the issues others have raised. My biggest concern going into the Beta was stability. In the Alphas, the game usually crashed somewhere between turn 270 - 290. Well, I can happily report that I am on turn 512 on a large map with everything set to common and I've had only one crash to desktop in the ship designer, which I was unable to repeat. Good work Stardock.
For me, one of the biggest draws to the GC games is the ship designer. After playing with it in Alpha, I could tell it wasn't up to the task of fine detail work, so I left it alone. So, I tried my hand at it in the Beta and it is better and certainly more stable. Because I like colony ships with rotating habitation models, below is my first ship in Beta.



What I really liked about the current state of the ship designer is that I can finally do detail work, such as the shuttles tucked under the spine and the "space traffic control" tower bottom forward.

Here's an in-game shot.

What is still problematic with the Ship Designer.
1) Mirroring does not work (at all) for me when creating my own custom parts. Each of the ring assemblies in the design above are a custom part, but I could not get it to work when I mirrored the support strut (the mirror property doesn't save). Therefore, I had to create two separate struts to make the ring piece work.
2) Mirroring still causes pieces to rotate opposite each other instead of in the same direction. Same fix as 1).
3) If I make a mistake saving a custom part, I cannot delete it from within the ship designer (or at least I couldn't find a delete feature). I now have several versions of the same parts, only the final one being correct.
4) The gizmo is great, but I noticed that after rotating a part, sometimes the colors would be wrong for rotating or offsetting the part again.
5) After I have modified the size of a part, any other part attached to it takes on that size characteristic. I'm not a fan of this. I had to attach all parts at their normal size first, then go back in and adjust each one. It's not a deal killer, but it is annoying.
6) At least one of the hard points still had an offset to it. The part had to be rotated 88 degrees to get it line up properly. I used to notice this a lot, but it only happened once in this design.
7) Because the design above uses the rotation animation, and uses counter-rotating parts, something strange happened while I was attaching the engine parts to the back end: I tried to mirror the engine part but the mirrored part would start moving in a slow circle. The fix was the same as 1), use two pieces instead of mirroring. Overall, the above design used no mirroring because the results were not desirable or predictable.
All that said, I am having fun and very much appreciate all the hard work you folks are doing!