Obviously, there are a million and one ways to improve a AI, so in this thread I am only calling out what I think are the most prevalent issues with the AI that with slight tweaks could give it a major boost in effectiveness. Here are my top 2 right now.

• Once a war gets going, the AI will just spam single ships, instead of placing them into fleets. This seems especially prevalent when its rushing ships, it just rushes out a single ship and sends it to its death. A better method would be to hold its ships in the stardock until its hit fleet limit. This has its own problems of course, but as a quick and dirty fix, I think that will make the AI much more threatening than the handful of single ships that just die against your fleets.
• The AI doesn't protect its transports, like at all. No transport should be sent to a planet without a solid escort.
• The AI gets obsessed with taking back its lost worlds, to the point where it will just send a ship to siege it...while I have a far superior fleet just parked next to the planet, ready to destroy it.
• Here is an example where the AI put the Galactic Bank in the corner. The GB has the greatest level bonus in the game, it should ALWAYS be fully surrounded by as many wealth adjacencies as you can muster, regardless of the planet's other features or uses.