Here's a list of all the problems that popped into my mind during a playtest. 12 AIs, High monster frequency, medium native frequency, 500 stars, 4-arm spiral:
Floaters are annoying.
Starvation system is iffy.
"Cannot Produce Ships, Can Produce Colony Ships" is both confusing and misleading.
Only Humans can starve.
Stealth techs don't do what they say they do.
It would be nice to be able to order a whole fleet to be built at once.
Monster Nests disappear too quickly.
Not being able to enqueue impossible items makes building shipyards kind of annoying.
Species randomizaition may be a bit off - there are like 4 Hhhoh.
If you select a fleet while the turn is being processed, you can't select ships in the fleet afterwards without closing and re-openeing the fleet window, or selecting another fleet then reselecting the same fleet.
Individual ships can't be dragged or de-selected by clicking on their stats bar (selecting works fine, fleets also work fine).
The order of effects for Ancient Ruins should put the Dragon Tooth last, so you're guaranteed to get at least something.
X PP and Y Turns means something completely different for ships than it does for buildings, in the header of the production screen. THe list of queuable items istelf though, is consistent.
Production Time is showing Never, even though it's going to be completed in about 12 turns and PP is being allocated.
Ships can't be scrapped in transit.
Psychogenic domination works on space monsters (not necessarily bad, just unexpected. Also, Floaters are annoying).
Sitrep messages that go onto a new line intersect other sitrep messages.
Solar Hull and Multi-Spectral Shield should give the same bonus and share a stackinggroup.
Up button isn't always available when it should be in encyclopedia.
Sitrep links sometimes don't work when they're on a new line.
Stargate is definitely NOT working.
With adequate tech, target meter values get to unreal levels, and the 3/turn meter growth you get from Force Energy Structures isn't enough to get the meter to target in a reasonable period of time (but maybe that's desirable?).
Xing out of a window overtop of the FO window causes the game to think the mouse button is being held down until it is clicked again. Likewise, clicking during turn processing causes the same problem.
After ordering a bunch of troop ships to invade, the fleet window resets to the top, but the troop ships remain selected, making it a pain to do other stuff with other ships in the fleet.
I got a crash upon trying to create a new fleet (once, not reproducible).
Fleet links in the empire section of the pedia don't seem to work.
Some of my newly conquered planets don't seem to be getting bonuses from buildings like Industrial Centers and Black Hole Power Generator.
Destroyed Buildings still show up in the Pedia.
Sometimes the numbers indicating ETA are obscured by icons of other fleets.
Sometimes there are famine messages even though there was no famine.
Player-owned Dyson Forests produce unaligned Floaters.
I think a couple of these things have already been resolved, but anyway...
One thing I was really pleased with is that even at the end of the game(~500 turns - I stopped when all monsters and enemy empires were destroyed), turn time was <10 seconds (though I had colonized nowhere near all the planets). That's a huge improvement, so nice work.