Very interesting thread. I wish more other games were critically analyzed like this. Too many forums succumb to the fallacy that criticism and complaints are evil...
Overall, I am very impressed with the AI. This is the best AI I've ever seen. In fact, it is one of the reasons I think GalCiv2 is one of the few truly innovative games (unlike the so-called "next-gen" titles).
However, the overall intelligence make the occasional flaws even more obvious. Much of what have been pointed out above is very true. Here are my additions:
1) Arceans went to war with me. Sent 3 fleets. I killed 1, but had to retreat. The remaining 2 reached an asteroid field with my unprotected mining bases... and turned back. I guess they were scared of my newly built military base, which was gadzillion miles away.
2) Erratic behavior in declaring wars. My best buddies, Korath, were in a distant corner of the map with a huge empty space between them and the rest of galaxy. They were constantly at war with at least 3 races. What the point, especially if the use super-slow ships? Also, sometimes they made peace with someone, and then went to war with the same empire (or the empire with them).
3) Not everyone liked Arceans. When I wen to war with them 2nd time, Drath and someone else gave me a couple of ships. The idea is nice, but those ships were SLOW, and they were on the other side of the map. Arrived just in time for my 3d war, thought. But that was way later.
4) Suicide attacks on economy star bases with fleets that could easily wipe my entire military out.
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Some suggestions. They would be quite difficult to implement, but I'll give the anyway.
1) Make AI to distinguish between different types of fleets. Some fleets should be fast. Other fleets should not. The lack of fast attack forces is definitely a big minus to AI strategy.
2) Make AI to distinguish between different types of wars. A war should be waged with some goal in mind, and that goal should be pursued continuously until it's no longer viable, or AI does not have any more resources.
a) Territory war. AI should try to capture and secure some conrete (i.e. useful to the AI) planets of the enemy empire. It should not try to wage wars on other planets, star bases or fleets.

Crippling war (when AI wants to retaliate). AI should target enemy's strategic points and easy targets. It should employ fast attack forces and avoid collision with major fleets or heavily defended star bases. It should destroy weak fleets, mines, unprotected bases. Capture/spore unprotected planet.
c) Total conquest war. AI wants to destroy the empire. Brings out all it can muster, engages in direct collisions with major fleets and star bases, tries to capture everything it can.
d) Reactive war. AI wants to keep other races from harming it's empire. Targets influence points and mines if influence is the problem. Targets military if it thinks someone is preparing for invasion. Makes appropriate demands in exchange for peace treaties. (I.e. give me this star base, or I'll destroy it anyway and do other bad stuff. Move away your fleet, or else. Destroy your star base...)
e) Support war. AI acts to help allies.
4) When AI has no goal or can't realistically complete it, it should not go to pointless wars across the galaxy.