Really enjoy the early access so far at around 10 hours in, so I figured I'd post a few of my early thoughts.
A couple of bugs I have seen are some battle viewer issues where missiles kill things before they actually hit, and missiles also aim wildly at starbases and sometimes the battle doesn't seem to end unless you click the resolve battle button. I also once had a CTD when the AI attacked me, I fought the battle, and then I was able to quickly select the ship and move it to fight another battle while it was not actually my turn, causing a crash on completion of the move (which I should not have been able to do in the first place). Other than those, so far so good.
On the balance side, the biggest thing that stands out to me is influence. My very first game (to be fair a tiny galaxy on beginner just to get my bearings), I won an influence victory without even realizing I was going to, and before any wars or anything. Since then i still find influence to be overpowered, as several times I have seen a planet get conquered only to flip control back due to influence 10 turns later. The UP resolution to stop influence flipping is a decent check on that but imo not good enough- their ought to be some way to resist influence flips, and not all planets should flip equally- it should be harder to flip a planet that has been under the other player's control for longer, approval should have an effect on it, or something. Other than that, I really just haven't played enough games to have seen other balance issues, but I'll keep posting as I play. My last thought is a concern about planet governance and the tasks for converting production to research and wealth, as those general seem far less efficient than simply changing the governance slider for that planet away from production, except in the case that the planet is extremely production specialized. If that's what those are there for, then great, keep them as is, I can see there being some use for that, but it may be a good idea to keep an eye on how often people are actually using those projects and tweak the rate of return accordingly.
Thanks for a great game so far,