Well, let me be straight up and honest.
Your documentation is lacking. Oh sure, your tutorial and manual covers the basics, and the wiki has a bunch of explanations, but it lacks many of the obscure mechanics that can easily make or break a game.
And even if the wiki covers it, it will still annoy people when they lose because they triggered an obscure defensive mechanic by the AI that your pretty much had to know about ahead of time to avoid it. Yes, it may be on the wiki, and they might find out what just happened to them there, but these important (like, you will quite likely lose if you don't know about them important) but you would have no idea if it you didn't read very detailed technical stuff or experience a loss (aka. trial and error gameplay, which is almost always bad design).
This can be a big deal, as if a new player loses because of a non-intuitive and not very well explained in game mechanic, AND the outside the game documentation (tutorials, the manual, and to a lesser extent, the wiki) does not make it clear that you should know this, that doesn't make new players think the game is clever, it makes them think that the devs are just making stuff up and "springing" on you for a surprise "ROFL-curbstomping", which you look like devs who can't keep their own mechanics straight, or worse, jerks. Either misunderstanding are great ways to lose new players.
Admittedly, the problem is much worse in the betas, but that is to be expected.
But here are some things that you need to know to survive (or have a decent chance of winning) but are very poorly explained in game and hard to even notice in the wiki until it is too late.
Solutions, hmm, that is much trickier. Maybe an "advanced" tutorial showing off some of the more obscure but "you need to have at least some understanding of them to stay alive" mechanics. Things like armor and how it influences durability, radar dampening, raid engines, alarm posts, border aggression, AI eyes, black hole generators, force-field immunity, and other things that can easily take a new player by surprise.
Also, there should be an "obscure and/or somewhat uncommon things to look out for or risk losing or making the AI near unbeatable" section in the manual AND the wiki, where they can get an advance warning about these things. In addition to what is covered by the "advanced", it should also list stuff rare enough not to justify putting in a tutorial but still can kill you if you trigger it accidentally (minor faction and AI plot stuff would belong here)
Also, continue work on the tool-tips. Many funny unit behaviors still don't have satisfactory explanation in their tool-tips
Here are some examples I can think of, in addition to what I listed for what needs to be put in an advanced tutorial. (Limiting myself to stuff in the last stable version of course):
Caps on defending AI ships per planet and what they scale with: I know that the number of defending ships that can be on any one AI planet is proportional to the number of guard posts, but this isn't clear at all from either the tutorial or the in game documentation. As such, you wouldn't know why neutering can be important until it is too late (all your border planets get surrounded by near impenetrably defended AI planets), and you have to come to the forums to ask how to deal with situation and then you find out about neutering.
Freed ships waiting on the other side of the wormhole: It isn't explained very well in game why AI units tend to "ball up" around the other side of the wormhole. The intuitive response would be to send more defenders to that planet, in fear of an immanent attack. However, thanks to the not very well explained behavior that the AI will wait until it thinks it has a decent chance of winning (thanks to firepower calculation shenanigans), these extra defenders make the challenge worse. The right responces are either to plunge into enemy territory and take out what you can and then pull back to take care of what went through, or to pull you ships to another planet to "bait" them into the planet, then come back in and crush them. Neither one of these is intuitive, but there is nothing in the game to explain why the intuitive solution is the wrong solution.
The "slowdown and you can't unload here zones" that you hit when you are far away from the center of the planet: No further explanation needed.
Hybrids: How they work is very, very opaque. As such, if a player takes the intuitive strategy with them (take some extra time to build up more defenses so they can survive hybrid attacks), this hurts them in the long run. Thanks to how caps are tied to hybrid spawners, the proper strategy is to find these spawners and kill them decently early in the game. But this connection of hybrid caps to spawners, or even the existance of spawners, is something that is not clear at all.
Fallen spire event attacks: I frequently find myself hesitating to build something new with the fallen spire campaign units (especially the buildings), because I don't know whether starting to build it will cause the AI to send out more event attacks.
This bit me in the butt the first time I played the campaign. When you build the scanning thingy from the first shard, no new event attack is spawned. As such, I thought that if you get the shard to your home, take out any lingering threat, and then start building what the shard gives you on your home, your are safe. Then imagine my unpleasant surprise that this does not hold for the second escort mission. In fact, the wave that spawns when you start building the spire colony ship seems to be even more brutal than the one you got escorting the Spire survivors, and there was no warning about it. Because I thought I was safe, based on my experiences from the first shard, I thought I could build it while my defenses were rebuilding as well. ...Yea, I was wrong, DEAD wrong.
It gets worse, another event attack is spawned when you place a city hub, and when you start building the first Spire reactor on a planet. All with no warning.
Yes, I understand that you guys are limited in man power, but non-intuitive, unclear from in-game sources, or you wouldn't even know about it until it is too late stuff needs to have a clear warning somewhere, or new players will be driven off.
Yikes, this post has gone on for WAAAY too long. I'll stop for now.