My apologies to start: many of these have likely already been reported.
I'm playing on a huge (as big as it will go) map, with abundant stars, planets, etc., and common or occasional everything else. Slowest research (-50%) possible. Max races. Custom race based on the Terrans.
General Experience
I've only had a few crashes. Trying to load a game while in a game often causes it to CTD. I had one repeatable crash caused by an unarmed surveyor ship (built on a cargo hull) encountering pirates in between turns (it was on auto-survey). Auto-resolving or "starting" the fight both just hung. I eventually loaded an auto-save, and moved the ship in manually, and it worked (yes, ship died; I'm a doofus).
Game is getting chunky / slow now that I have exploratory treaties with a bunch of other empires.
It's taken me a bit to realize not to fill up a planet with all the buildings first, as it'll take forever to develop. Built the core factories, let them build up to max level, then work on everything else as necessary.
I wish the game automatically cancelled any "forever builds", like Research project, birthing studies, etc., either after a set amount of time or when new buildings become available for the colony.
Some of the space junk looks similar to duranium. I've occasionally accidentally tried to build a mining station in the middle of nowhere when I wasn't paying close attention.
More information regarding approval would be nice; I haven't been able to find anything to tell me why (or why not) my colonies are happy or sad.
Please provide an option to prevent computer-designed ships. Right now, every time I research something, I get 20 new designs, none of which I want (I prefer my own designs). Tedious to remove, and futile as they'll come back in a turn or two.
Diplomacy
Very broken right now.
I can offer multiple "free trade pacts" to the same empire, and they give me stuff each time.
Likewise, getting to #1 militarily allowed me to extort all of their credits, techs, and over 400 creds/week from every other empire in exchange for a non-aggression treaty. Way broken.
One-off treaties can be later cancelled, for some reason (i.e. exchange 100 credits for a tech, it shows up as a treaty).
Some of the leader relations bars are smiley faces, others are X's. No clear indicators as to what those bars represent.
More feedback regarding the United Planets initiatives would be nice, such as an indicator saying who is the empire with the most credits for the one where they'd have to give away some of their cash.
Ideology
Really easy to get. I seem to get one new ideology every time I colonize a planet. And on a huge map, that's a lot (at 40+ colonies atm).
Random events don't seem too onerous, either way, to dissuade me from taking whichever one advances my ideology.
Benevolent's free planets boons don't seem to be WAI. The size 10 one gave me a 13, the size 16 one gave me a 6 (!).
Combat
I haven't gotten much into combat yet. Seems more interesting than prior GC's, though lasers seem by far the best atm.
Overall, liking some of the directions that game is going in. The universe is busier, with all the resources to mine. It's shinier, and planet building is somewhat more interesting now.