First of all, this is shaping up to be a great game, I also played some new StarDrive II and am frustrated by certain game mechanics in it.
But it's not there yet! Here are some of the strange things and bugs I found after some intense gameplay as a custom faction
- Savegame issue: I still have problems simply saving the game, a ~ will show up in front of the given name, and I have to edit it to be able to save a legit savegame
- Techtrade issue: Drengins wanted to trade with me, and suddenly I was able to trade tech to them which I certainly didn't research?! :Like slavepit tech etc.
- Minors starbase trade prob: I traded a starbase with a minor race to get some peaceful acces to certain resources. But the funny thing is, they were attacked by another major, were destroyed and suddenly the base I had received didn't produce any minable resources anymore??
- Minors conquering and colonizing?: Don't know if this IS a bug, but I suddenly saw minors expanding, and picking up yor planets after I was crushing them and they had left a lot of planets undefended. Now I do not care if that is accepted behaviour, accept they don't have any culture penalties so can exist in my influence space 
- Pathfinding ship grave yards: Sometimes the game crashes on entering anomalies especially ship grave yards defended by pirates (which are very easy to defeat), I can understand..it's a beta, could also be a memory overflow when other big scale events are scheduled in the same round..but what frustrates me is that other survey ships when automated simply keep visiting the sites even when I said NO don't visit to the first ship 
- Upgrading ship errors: I know, updating ships is an insane business at the moment, costing you a lot more then simply building a better version (hope this will be adressed, because else why put the option in?, already heard Paul talking about it) but sometimes I was unable to update anything f.i. a warhammer and the only updates possible where 30 surveyship hulls??
- Unable to declare war: Ok this is my biggest frustration at this moment, I am building fleets, transporters at the ready...I want to declare war....and......not possible??!! I don't have any treaties have deleted any possible trade routes, and still not able?? Wondering if this has anything to do with being chairman of the UP, or sharing affiliacy? Or maybe it has something to do with them initially colonizing in my territory, losing that planets due to influence/rebellion and somehow still being part of my empire?
Furthermore I am experiencing some inconsistencies like: building the same type of transport and on the one shipyard I am able to fill it with 6, and on the other just with 3? Certain starbase modules are listed as a possible upgrade, but am unable to select them ( I mean if the technology is not there yet, why show the option)...and the funny thing is, on certain planets I AM able to select them.
Well there's my first list of items, will update it when I come across something new.
Update 17/4
It seems like there is a problem concerning population growth, I have chosen infertile as a race traith (-15%), but I even researched abundance and still growth will not go over 0.2 no matter how big and lush my planet is. And also not keeping current population in mind ( I mean on a planet of 5.2 the growth is 0.2, but also when my planet already reached 20.3 it keeps at a slow 0.2 per turn)
Also: Races do indeed start building starbases to mine resources in .82 (also in my territory), but they ignore the relics (but I guess that's a known issue)