I put down wonders and tech tree as problems, but both I think are more a matter of scope (and development time) rather than true game play problems. I mean, it would be more fun to have more scifi options to play with and wonder races to compete in.
The AI, though, is a problem. First issue is exploration -- units will happily move into hostile/lethal terrain if exploring. I'd guess this is due to looking many moves ahead and not testing for moves which leave units in lethal terrain. OTOH, fast units can safely traverse black holes, so part of the problem isn't lethality, but movement speed. A unit with two moves, which finds itself in a bad square, could move one more space to safety. This presumes that the movement routines can cope with newly spotted hazard terrain.
The second is the AI inability to use squadrons and missiles on carriers, starbases, and cruisers. This cripples its combat capability compared to a human. The game's AI can't cope with land units (which is what FF spacecraft are) operating as carriers, at least for now.
A last issue is stealth ships. The AI can use them, but does so rarely, and has no defensive strategy against them. A simple solution would be to deny them pillaging -- they'd still be a hazard, but wouldn't be able to go about destroying infrastructure so easily. If they AI did use them, as a human can in a multiplayer game, intelligent scouting defenders would limit them, but they'd still be a pain to cope with.
Another issue is balance. First, between the factions. Different but equal is a tricky goal to achieve. Having more factions wouldn't totally eliminate this, but would offer more combinations of allies to perhaps weaken strong factions.
Second, the combat balance and price to performance values of the units isn't ideal. The delta upgrade is generally worth the double price of the unit, but the omega upgrades tend to be expensive. They are too expensive for the top three units -- omega cruisers, battleships, and carriers are simply not worth the price. And given that you must spend a lot of research to get them, that is a serious game balance issue. A smart player can simply build two delta units and get more bang for the buck. The omega squadrons and light ships are fairly decent in balance -- 6 for delta vs 9 for omega (and generally a point of speed/range).
If delta to omega is a 50% increase, then the omega battleship should be 36 x 1.5, or 54, at least. But given that it is the ultimate brute force weapon, and is extremely expensive, an even greater advantage is justifiable. As it is, you are usually better off using two delta battleships. It needs something more to be worth the cost (plus research) of two of those.
Carriers are the worst off. The delta carrier is just slightly better as a squadron platform than the basic model, with a gain of speed which is nice but not essential. The omega doesn't offer a speed edge over the delta, nor does it give twice the squadron firepower. Overall, you are better off with four basic alpha carriers than either two delta or one omega. Twice the squadrons of an omega, and able to be in four times the places. The cargo promotion only amplifies this edge, as your early build carriers can fill all your needs.
As galactic domination is the ultimate and very expensive military tech, it is a shame that the unit you get isn't worth getting.
Cruisers are relatively weak units, compared to destroyers which tend to do the same basic job. You need few of them to deliver missiles, because you'll only have so many missiles to play with. Their basic combat power isn't hot enough to justify their cost. Their position in the tech tree is fairly close to the destroyer advances. A delta destroyer is generally more useful than an alpha cruiser, and likewise for omega vs delta cruiser. The Omega cruiser is nice in combat power compared to the delta cruiser (unlike the omega battleship), but its missile carrying power isn't that special.
All in all, it makes the top three military techs of dubious utility. You should be able to win a military campaign without them, and beat up someone who does go after them.
I've been testing mods to change the combat values. I'm not quite done yet. My current thought is like this:
#1: omega to delta combat ratios are generally 1.5:1, with other bonuses factored in.
#2: omega should be one movement more than delta. This is the case with some units now, but not all.
#3: cruisers should be half battleship strength. That's enough to blast destroyers and lesser ships of one generation higher, and helps justify their cost without missiles. Missile capacity should be 50% higher per generation, roughly, though higher combat power could reduce that for balance.
#4: carriers aren't cool enough (or useful enough) if all they effectively gain is squadron capacity. Rather, let them evolve into hybrid direct combat ships. delta is like a destroyer/cruiser combo, omega like a delta battleship/destroyer combo (or battlestar). Coupled with speed gains (move 3 for omega), this gives them a strong place on the end game battlefield, and a strong reason to get and use them. A 4x squadron capacity (12!) doesn't mean much if you can't field that many squadrons, and can't let your carrier actually engage in close combat.
#5: I'd like to give at least the omega battleship a starbase-type ranged attack. If I don't do that, i think that a move-2, strength 60 unit, while fair for balance, will still be overwhelmed by squadron defenses. Giving it more raw combat power or speed would also work, but not be quite as good at representing the "death star" idea of slow but lethal.
#5a: If I can give the omega battleship a ranged attack, I'd boost the cruiser speeds to 2 (delta) and 3 (omega). Omega cruiser should require alloy, just like omega destroyers, which would slow the tech tree on the military side.
A side note on speed: The mobility promotion reduces the need for speed upgrades, as your move-1 units will move 2. I try to give that to my battleships, so that I'll have a fleet which can move at 2. Even if I get speed 3 capability later, it is difficult and expensive to make the entire fleet move that fast. Because of that, move 3 isn't as impressive as it could be. You need to use only fast units in a fleet to take full advantage, and that means the latest and most expensive. Otherwise, they are limited in effect to a move of 2. The AI doesn't seem to use the movement promotion much, but it really helps battleships.