Okay, I've played a few games already in ver. 1.1 of GCIII and here are some issues and bugs I've noticed. No doubt many of these have been pointed out already, but these are ones that I think I stood out for me the most.

• I noticed that sometimes white bands would show up on the interface screen over the font. This is something that happened in the previous version too. I noticed that this only happens if I repeatedly leave a current game and restart a new game from the main menu. The problem goes away if I exit the game completely and restart it.
• I get stalls sometimes. In between turns, it will suddenly stall with the caption on the "next turn" button showing "Idle Ship" but greyed out. If I press the button, nothing happens. I'm able to solve the problem by saving the game and reloading it.
• The AI isn't very smart sometimes about attacking starbases. Essentially, they're too stingy. I noticed that the AI will be reluctant to attack starbases if I have some good defences in place. However, while an individual AI fleet may not likely destroy my starbase in one shot, it could do it easily if they attack it in waves of fleets. There was a time when the Yor had a huge number of ships and fleets around my military starbase, but they didn't attack it. It appears that they only want to do it in one shot and they refuse to sacrifice even one fleet to weaken it. Two waves of attacks would have easily destroyed the starbase, if they wanted to.
• This has been mentioned before, but the animated battles often do not reflect the actual outcomes. For example, I'd often see cases where I'd lose 1 ship, but when it returns to main screen, I find that I actually lose 2 ships instead.
• If an AI declares war on me, and if they're far enough away, I usually have nothing to worry about. The AI simply won't attack me at all and won't even bother taking steps to empower themselves to. I can understand that this can be a problem for them if another empire is in their way (especially if they're at war with them), but that's not often the case, I think the AI could at least do something like building starbases or make warships with greater life support capabilities to extend their range to attack me.
• Elerium is really, really rare. I usually can't find any elerium at all in most games. In somes games, elerium does turn up and I think appearance depends on what map options I choose. I choose resources as "uncommon" as an option usually. I can usually find plenty of duranthium, prometheum, thulium, and antimatter, but elerium is either incredibly rare or non-existent.
• Wars are really, really tough to end. Unless I'm beating the crap out of an enemy AI, getting some sort of peace arrangement is near impossible. Even offering a huge payoff via diplomacy won't work. Perhaps that was intended? 
• I mentioned this in a previous post, but when AI ships depart a plant, they are vulnerable to attack because they won't group into a fleet. When I do it, it's automatic. But for some reason, when AI ships departs a planet, they're individual units.

Anyways, there are other issues I found, but the ones mentioned here were the most prominent ones.