In my current game (Insane Spiral Map, Abundant planets, 15 AI including some customs, Gifted AI, playing as a custom race), I had a few strange things occur. Not necessarily bugs, though in some cases bad ones, and opinions on the way things have played out:
1) *some* AI's don't expand. Not sure why; AI focus? When I met the Humans and Altarians, I had about 100 colonies. The humans had 2 (Earth and Mars), the Altarians had 7. Several others were on par with me, but for the most part it seemed only about 3 or 4 races actively expanded (Krynn, Iconians, a custom race that is built for expansion). Once I met them, they started to expand (humans are up to ~20 now).
2) Faction Power is pretty meaningless. My first war (against the Krynn) saw me going against someone with almost twice my faction power. I thought I was in trouble, but it turns out they were pushovers.
3) AI don't like fleets. One of the reasons I was able to win, was that the AI kept sending in single, large-hull ships, that my fleets could easily pick apart. Occasionally a small two-ship fleet would come in. They had logistics (30 I believe, enough for 4 large ship fleets), even sometimes having four solitary ships adjacent to one another. The only times they made full fleets was to protect their unarmed transports.
4) Shipyards need some defensive buffs. Shipyards are way too easy to destroy, especially mid-game. Starbases get all sorts of defensive upgrades, which can make destroying them painful or damaging at least. Why not shipyards? I found it way too easy to send in fast fleets with enough firepower to destroy their shipyards. Without shipyards, an empire can't do anything, and you can attrite all of their existing ships. Maybe have shipyards gain automatic upgrades like carrier fighters do? Why are starbases much easier to defend than the more important shipyards?
5) Carriers are OP. Mostly because of their auto-repair/auto-reinforcement/auto-upgrades. It's hard to accurately judge though, as I'm technologically superior to those I'm at war with, and they don't really form fleets (see 3).
6) Ship repairs are sooooo slow as to be non-existent. Is there some way I'm unaware of to speed up the repairs?
7) Combat regen bonuses (self-healing hull, for instance), are really underwhelming IMO. By the time it's relevant (i.e. you're taking damage in a battle), you're taking much more damage than the thing heals, as your defenses are down so you're taking max damage per hit. Especially when they cost resources/ship space.
8) Diplomacy is still wonky. Do free-trade agreements help both parties? I can offer it, and the AI seems to think it's a gift. I've gifted the technology to other AIs, but I can never have them offer it to me. Also, things like open borders, non-aggression treaties seem to expire or cancel randomly. Some sort of notifications would be nice. I've also never had the AI approach me about a deal; I've always had to initiate.
9) The forced trade cooldown is just annoying, especially as I have no idea how long you have to wait (some sort of notification in the diplomacy window, maybe?) which means I have to check back every turn for every AI to see if they're willing to trade now.
10) Crashes. It crashes fairly frequently now (every 3-5 turns or so), late game. Early game was fine. I think I got some 40 hours in this game (currently at ~70 now I think) before it started crashing frequently. Things that cause crashes sometimes: accessing Timelines, opening trade with Iconians, accessing Graphs. Biggest bug so far is that I cannot trade with the Iconians. They're the largest empire (over 160 colonies, when last I could see). In the trade window, all that shows is Offer Credits and Credits per Week, and a non-functioning scroll bar. Everything else is blank. I can offer anything (colonies, tech, etc.).