Some thoughts playing 1.03 with a custom civ, some already mentioned:
Never got any of the prototype ships even though some like the Praxis were awarded over 20 times, got all the Retribution pieces and had the dialog saying it was available but never showed up at shipyard.
When deleting improvements on a captured world, a black dialog box shows up and obscures part of the page until you click somewhere outside of it
Had massive amounts of Thulium and Promethion, over 500, but very little Elerium and anti matter never more than 10 at any point
90% of ship graveyards gave explorer ships which were able to survey Precursor anomalies without any issues on "automate" so by turn 350 I had gained 11 (+10%) manufacturing bonuses without any fights while most of my human guided survey fleets who had to fight the anomaly ships got the +1 antimatter bonus
Planets over size 5 should give a better set of bonuses when left as colonies otherwise it makes no sense to leave them as such and not transfer them to core worlds.
There should be a way to gather core worlds resources into designated shipyards again, I find that even on common planets you end up with shipyard spam
Growth is definitely slowed as the game persists, by turn 350 most of my planets still only have 9 or 10 pops even with room for 35 on some and maxed out growth rates
The AI makes no use of improvements, all the planets I invaded only had districts on them with some peculiarities like some with no capital and most with no entertainment district but maxed out (96%) morale.
On a long game with max size galaxy, 22 opponents and common everything, by turn 250 it takes quite a while to resolve the AI turn even on a good PC, that is understandable and better than with GC3 but one slightly annoying issue is that when a tech is researched the window to choose a new one pops up before the computer has resolved the AI turn and you are stuck on that page until all AI players have finished, that can be a while with 22 opponents at turn 300 and on.
Ideology points are a bit hard to get, would like more opportunity to explore the various branches
Need more ships we can assign commanders to. The concept is great just limited since we only get a few ships to use, no Huge hull ships as far as I could tell in my game using legendary ships, maybe the opportunity with a certain tech researched to gain access to other ship types or the types used by conquered civs?
Would like to see more improvements as opposed to district level up's for planets, game is fun until about turn 200-250 until you rule your own huge sector but then it becomes a bit tedious with just levelling up planets and trying to capture other sectors, the first one is interesting but after that it is just an endless repeat. The mid and late game are missing something to spice it up, previous games had the Dread Lords and such but even then that was a bit underwhelming. To be fair this is a common issue with 4x games so not sure how to spice this up, the early to mid game are a ton of fun and becoming master of your huge sector and even one to two others is a thrill but after that it is just tedious. Maybe having influence creep into other sectors, discovery of tunneling techs to create shortcuts between sectors, absolutely bonkers civs that can only be discovered when you breach sectors far from yours who have overwhelming and alien tech that can only be stolen from their ships or developed by combinations of researchers from several different species. Something to shake up the mid to late game on large galaxies.
Overall 1.03 is a great leap forward and the game is headed in the right direction. Looking forward to 1.04 
