I've now played the game against Genius AIs (still have to play against Incredible) but I noticed it doing a few things wrong that it also does on the Bright level. I feel these are fairly obvious mistakes to be avoided...
1) The AI never builds farms. This not only means that the AI has a limited revnue base to do construction and research with, but also that its' worlds are that much easier to conquer, because they all contain either 5 or 10 billion people.
2) Maybe the number of troops to land on a world is hard-coded, rather than dynamicly determined, but the AI almost never invades my planets with enough troops to take the planet over. I usually have 15-22 billion people on my planets, and they are pretty capable at fighting off invasion after invasion of 1000-2000 troops. On the flip side, I figure out how many troops are needed to defeat a given enemy, and tailor-make my troop transporters to carry just enough soldiers to obtain victory.
3) The AI builds Super-Projects on top of special resources... particularly food and morale. Maybe these aren't useful because it doesn't build farms, but I find these to be crucial assets within my own empire. (It is also annoying that these can not be dismantled. Sometimes I'd rather scuttle on Omega defense to get a +100% morale resource on a conquered planet.)
4) The AI doesn't seem to specialize planets depending on the resources found there or the size of the planet. It seems to build fairly similar items on all planets. A few times my spies have revealed that various types of capitols have been constructed on Class 7 or 8 worlds when the AI has a a Class 16 that would have made a much better choice. Likewise, the AI will sometimes build more than one type of capitol on the same world, limiting the full advantage of utilizing that capitol with buildings that are synergistic with it.
5) The AI trades technology a little too willingly. I don't like disabling tech trading, because I think it is a cool (and pseudo-realistic) part of being a space-faring civilization. However, when I play, I choose a few races I want to be friends with and am more willing to trade tech with them. Maybe if the AI stuck to the couple races that they had the closest relations with, or just their allies, instead of trading with everyone, a happy medium would be found.
6) The AI trades technologies with a galactic achievement before they build the galactic achievement. This is something I never am willing to do unless I'm desperate for credits. Generally, the biggest advanatge of developing a technology like Habitat Improvement, is the ability to get Aphrodisiac reliably. The galactic projects offer huge bonuses for a civilization, and the computer should protect this advantage as zealously as I would. (In Civ IV, the computer is very good about this.)
7) The AI doesn't discriminate between which technologies it trades. As a player, I am always more willing to give up a technology I know other races have because I know those other races may also trade it away. I usually have a list of technologies I don't want to share, and just don't trade them with anyone else.
8) Maybe some of the AI races (like the Diplomacy heavy humans) should get a tech-trader flag, that makes them buy and re-sell technologies as much as possible. Kind of like the Militaristic quality, but instead of aggresively attacking planets, they aggresively buy and re-sell technology throughout the galaxy. This would be another good alternative to disabling tech-trading: making the computer fill the role so that the player has much less opportunity for advantage doing this.