So while playing I feel like I found some major problems. Declaimer, I'm sure these have probably been posted else where, and I may have very well missed something and that is why I feel like they are oversights.
1. Basic tooltips, but I'm sure this is something to come later
2. Population Pressure. This destroys your approval early game and there is no way to stop it? From my understanding you have higher pop pressure the closer you pop is to your max, and at max its -50%. If this is how it works this is insane. The only early game solution, before lots of tech and approval buildings, is to increase the pop cap with food, but eventually they will reach that cap again and screw your approval. Not a huge late game problem because tech can overcome that, I assume. I'd suggest allowing the player to enforce a custom pop cap for a planet, or make the negative approval from pop pressure scale. For instance if they are at the cap of 8bil -10% approval, cap of 12bil -20% appoval and so on. Just example numbers here.
3. Early fighters killing shipyards, and a lack of ground shipyards (I know this is posted elsewhere). This can completely screw a race over within a few turns. This one kinda speaks for itself. Also, this makes it very hard to play a game where you want to take a backseat to war, one of the play styles I personally enjoy. What I mean by this is a game where you sit back and espionage, or trick people into war, or play a mercenary that sells off tech and ships to warring races. I LOVE that fact that you can play like this with success in previous titles. But with the change to the shipyards you constantly have to have a decent fleet ready to defend your shipyards. You can play that "peaceful" trickster all game, but the second a race turns on you, they whip our your shipyards and you are just totally boned unless you have a large standing fleet. AKA bring back the option for planet shipyard. I love the idea for space based shipyards, but there is a need for ground based ones too.
4.Next turn button. I like the feature of showing/cycling through idle ships, research, planets, etc. but don't force me to make it perform an action. Its possible I could have turned off the "no idle anything" feature somewhere, but I couldn't find it. Maybe I don't want my this ship to be moving or have and AI control, but I can't go to the next turn unless every ship, planet, etc has and action to perform, thank you for showing me, now let me move on. The shipyard part is absurd. It HAS to be making a ship? It HAS to be sponsored by a planet? What if I don't want more ships because of the upkeep cost? What if I don't want a sponsor because I don't want it to negatively affect a planet? (Assuming there is a negative effect, like lower build times on the planet, if not there probably should be). End the end, thanks for showing me my idle stuff, forcing non-idle planets and research is probably fine, but forcing non-idle shipyards and ships, eh...
Again, its possible I missed some things and these actual aren't issues at all, and I understand its a beta and everything is a work in progress, trial and error at times. Just my opinion.