Just finished my first play through of the beta and I have some suggestions, comments and a few of bugs to report.
First the bugs, I didn't notice until late game but every time I hit add sponsor to a shipyard the game crashed. At one point I mistakenly build a second shipyard(although from reading the forums that seems a feature not a bug, building multiple shipyards at a planet) and when the orphaned shipyard came up I had to reload the previous turn to avoid it. I don't know if this started later or was from the start of the game.
The second bug was that every captured planet came to me with -50% wealth approval. If that was intended I'm not a fan, maybe if the planet launched a ship carrying the wealth of the planet that I could catch or if it was my planet could be brought back to a friendly planet to give it a boost.
It seems like some of the one per planet or 1 per civilization improvements aren't disallowed as they should be, I ended up with a few captured worlds that had a colonial hospital and the second tier both on the same planet. Also I captured manufacturing, entertainment and technological capitals all the time and I generally killed them because they didn't seem to work. I assume the first one is the one that stays and the rest the bonuses show up but aren't applied. A warning of some sort for them would be nice.
Another issue I had was I had a few conquests revert due to influence but only got one influence conversion mid game. At the end of the game however I had several enemy well inside my influence that never changed, I specifically left them to influence conversion sending my transports to further conquests assuming they would shortly become mine. After something like 30 turns they still hadn't converted. I address below that I didn't go as far as I could have in the invasion or planetary defense lines as they didn't seem to be worth it so maybe they had something there that prevented them from turning I didn't look at.
Next suggestions, wealth, approval, and population are out of whack. Wealth and approval bonuses are low and population is more important that any other factor early game and once the other bonuses catch up gets a bit ridiculous. These just need to be adjusted but that's the point of this part of the beta, I'll leave this one to your big brained math guys to figure out although I would suggest not just using %s for the bonuses as it tends to make the early game tedious and late game overpowered.
A bit more on the wealth issue, once I had my empire starting to roll I researched I think it was tier 3 manufacturing and my economy crashed from the upgrades. I think I was getting about 20 credits per turn down to -100 or more per turn. An upgrade should not crash my economy. Although while I was waiting for all those factories to upgrade I researched tourism and the cash flow problem went away but my approval was still in the gutter and plummeted every time I had an upgrade.
Idle shipyards at late game get a bit out of hand, I hadn't micromanaged too much early game and it caught to up to me when colonization was no longer a viable expansion option so I ended up with a ludicrous number of shipyards that just had to be fed constantly when I got my economy going and I was pumping out a ship every 3 turns from industrial powerhouses and even the marginal ones were annoyingly productive. I can pass with ships please add that functionality to shipyards even if its for late game.
I liked the idea of 3 techs for miniaturization, cost effectiveness and increased effectiveness for many things but later in the game it seemed more like it was a delaying tactic to reach the end of the tech tree. My suggestion is to lump them all into one and set the cost between 1.5 to 1.75 the cost of one of them.
I know the AI hasn't had much work on it but spend a day or 2 to stop it from building the various capitals on every freaking planet please.
The ship combat made no sense to me, I was using large ships when the AI was using smalls to mediums still and I could take out 1 of the mediums with no damage but if I took on 4 medium with my large I traded 1 for 1 even though I went heavy on the defenses and had the same defense rating as their fleet offense(missiles and point defense) and I had more hit points in 1 ship than their fleet. No idea what went on behind the scenes to give those results but I went more offensive and it didn't seem to make much difference other than I started making more medium ships and wasn't overly upset at loosing so many ships. Also yes I realize that many attackers on a larger ship would have an advantage but I expected to at least damage or destroy a second ship especially going so heavy on defense.
Capturing colonies was a bit ridiculous as well but I expect that is part of the point of this part of the beta as well but population(again) seemed to be the defining factor in whether the invasion was successful or not. Tech didn't seem to make a difference even though some of them were left in part of the beta, I noticed that later portion of the tree were disabled.
Comments, this section includes some personal politics so feel free to ignore it or keep it for GalCiv4 in a few years.
Less political suggestions first. For star bases that are economic based I think it would be really cool if they have population as well as crew and treat them as small artificial planets, maybe even including a shipyard as well rather than just giving bonuses to nearby planets. I would say let them get bigger as ships get bigger(although I would think the stations are already much bigger) and maybe allow them to be sponsored by mining stations to be more productive. I would also really like to be able to do something with asteroids, mine them, from a planet or station for wealth or production, maybe throw in some asteroid mining techs, like inflated asteroid stations that would allow large populations on stations. Or with greater technology allow really big stations that can be dual or triple specialized maybe allow everything to be put on them, turn them into ring worlds or Dyson Spheres. I would like a lot more orbital industry but of course its a big target at war. That might even allow for deeper diplomacy. "That's a nice system you've got there be a shame if a warship got in there and wrecked it all."
In a similar vein of asteroid mining gas giant mining planet or station based, generally they are used to fuel fleets in scifi, I would love if you did something cool with gas mining. So having them gives a bonus to range or speed of ships
I realize some of the old timers will scream at this suggestion but isn't it time to move past some of the aspects of 4x design that might not be the most fun? (Here's the politics part although part of it is I don't think its fun either) Why is it assumed that the government is responsible for the happiness of the people? We are playing head of state so in game we are the gov't, my argument here is that first I don't like this aspect of the game, let them hate me for my policies not that I don't provide bread and circuses and I realize this takes a lot more effort in design and would take the genre either in a new direction or just kill this part of the game but I also have a personal dislike and distaste for the idea of government provided "entertainment" as well as I assume a lot of the development costs of this game are covered by pre-orders, we as private citizens are providing for our own entertainment and private companies are stepping up to fill the gap that we demand the game.
Overpopulation, another part of the approval game I don't care for. I'm going to assume that most of the players of this game are westerners and for us living close together gets bothersome but not all cultures on Earth feel that way, most of the rest of the world has a much smaller personal bubble and most likely we prickly westerners would be the first on the ships to get to a new world of open spaces. I don't think population pressure should be given so much emphasis and there are a few ways around it as well. First the prickly, get out of my space types are most likely the ones that would be on the colony ships again and again so the people that don't mind living so closely get to stay on those highly populated worlds. Second as we become more wealthy and industrialized we stop having so many kids and automate a lot of manual labor. I suggest that half of the population growth techs be moved over to robotics techs, more manufacturing done by robots, and rather then needing lots of people to work in factories, a lot of people program the robots, a few maintain them and a few run the factory. Same with farming but not research, that requires human intuition, trying to figure things and sometimes screwing up. So further I would suggest that high populations shouldn't be the norm for most societies but maybe a race or two would prefer to use slaves or lower class/caste rather than robots for manufacture. This could also fix the population trumping other factors and allow small planets to be worth the time they need to be productive.
Wealth really should be taxes and shouldn't be a research line. As it stands in the game it kind of works that way already, generating money takes away from manufacture and research but(politics again) government doesn't create wealth, at least for humans, communism doesn't work well for us but maybe for aliens it does and keep it like that for one or more of them.