I decided to run a normal game before diving into the campaign, and have spent about 125-130 turns on a huge spiral map against gifted AI's, playing a custom Iconian faction, and noticed a few oddities. Some of these may be working as intended, but it is difficult to tell.
First off, there were instances when Drengin ships and shipyards simply disappeared during our conflict. They didn't move off into fog of war, they simply were gone. It's possible they were decommissioned, as I know the AI has had a habit of such things in the past, but if so, it wasn't for good reason.
Second, I received no science bonus from the Quantum Leap Ideology buff. I got the research points (600 or so), but those are laughable, the only reason to pursue that branch is the +5 research bonus to each colony, and I didn't get any bonus at all. Disappointing to say the least.
Next, Tactical Healing seems both broken (as in bugged) and broken (as in OP). My healing hulls shrug off damage at an amazing rate, making enemies fall before my ships with ease. However, on the rare occasion that I bite off more than I can handle and actually take great deals of damage (an total amount up to the total maximum HP or above, even though it has all been healed back), the battle viewer counts the ship as dead in the upper part of the display (taking away their combat power from the bar) and, from that point on, the ship stops healing, though it does continue to participate in combat. It is possible it is working as intended, but it seems buggy to me.
On one occasion I used a constructor with multiple modules to create a shipyard. Doing so consumed the entire ship, whereas creating a starbase with such a ship leaves the ship intact (though minus a module).
Whatever has happened to the Yor, they make money like no tomorrow. I find it easy to exploit them on trades for extra cash when needed.
The Paranoid racial ability doesn't count, politically, as having defenses. As a result, you are still 'ripe for conquest' if you don't spend your production defending your planets like normal. It makes the racial ability much less useful than if it were taken into account by the AI.
The AI still seems to be playing with unexplained knowledge of the map. On several occasions, I noticed AI players sending colony or constructor ships toward planets or resources they never discovered via scouts, etc, and even noticed some of them turn back ships when planets or resources were claimed, even though they had no way to see it happen. It doesn't seem to be universal, as there are still several planets far in the corner of the map that I have not yet taken, that the AI hasn't made a move to (they are out of influence as well), but it would still seem to be a limited degree of map cheating.
The Ancient racial trait doesn't seem to get any additional bonus for research relics, just the standard research bonus whereas they get the base bonus and a research bonus from all other relics.
Often times the movement speed of a ship or fleet seems to be missing from the displays on screen. This can be annoying as it is some of the most important tactical information you are looking for when selecting an enemy ship (or even one of your own).
The colony trading goods (the ones that fill tiles) seem to be giving stacking bonuses even though they claim to be one per civilization bonuses. My tooltip shows a +15% bonus from Precursor Nanites, for instance, of which I control 3.
Shields seem to be shot off during combat. As every AI seems to favor beams, I haven't seen how the other defenses are working, but as beam shots strike my ships, their shield stats drop (when the ships are highlighted during combat) and they take more damage until they show 0 shields and are taking full damage.
That is the weird stuff I noticed, other than the Iridians suddenly gaining more than triple anyone else's military power in a single turn, but I think that was the result of the pragmatic ideology buff that gives three defense ships per planet. Still, it completely destabilized my game with every AI doing nothing but producing military assets to try to keep up. Then everyone started declaring war non-stop, which was great fun. Not sure if that is how it is supposed to work, but that is what happened.
Love the game, overall it's very enjoyable. Look forward to what comes in the future.