I've spotted the following items and notes in the latest beta release (3):
1. Pop-up info boxes: these need to be expanded or set-up to scale; there are still instances where text runs off the top or bottom of box.
2. Terraforming Event: this event provides the option of gaining a tile in exchange for production reduction for 10 turns -- the terraforming never ends, and production across all planets remains -90% indefinitely.
3. Shipyard list of designs: we need to be able to remove a design from the list. I'm one of those that likes to create designs, but the list is getting extreme...
4. Star Names, Length: some star names are extremely long, and occasionally over-write the size of the planet on info pop-ups (ie, mouse-over text boxes). Example: Ghostprogrammer is one that ends up over-writing the planet size (sorry for whoever chose that name). Maybe adjusting #1 above will correct this?
5. Star Names, Repeats: my current game now has THREE Thulium stars. Obviously, some of the names are being selected twice. (I'm sure those of us who chose names cringe at the possibility of our star name not showing because colonists seem to like Thulium as a name -- after all, there's a Springfield in almost every state in the USA -- but perhaps the colonists can be overruled?) 
6. Blackholes: can still tell which unexplored stars are blackholes -- the top, bottom-right, bottom-left corners of the grid still have a dot in them when zooming out and in.
7. Pathing of ships in Nebula & Dust: when there's a artifact or other anomaly within a nebula or dust cloud, or when moving in one of these zones, the pathing to get to it is broken. Sending a survey vessel to the spot often sees the survey ship auto-moving to another spot in the nebula/dust. It seems the top-right hexside works often for an anomaly approach, but not always.
8. Ideology, Pragmatism, Reasonable: I know this isn't active yet, but I'm thinking "by turn 100" may be insufficient. At turn 124 in a game I finally had the points to select this, but 124 is past 100... perhaps the result should be peace for the next 50 turns or something such instead?
9. Freighters in other empire's zone of control: these are counting as negatives in diplomacy; should freighters be completely neutral, perhaps even a positive for diplomacy?
10. United Planets: can we see what our impact will be in decisions? We see how much percentage influence every other empire has, just not ours?
Positives:
A. Cutscenes are very nicely done; when they end, can you freeze the last image instead of blacking out the picture?
B. Very nice Event images. These really look great.
C. Looking good overall!
