I've just finished a 1.6 beta 3 DA match. Either I'm getting better or the AI gets dumber every game I play. I'm playing on Tough with maximum CPU usaged enabled.
There are a couple of things the AI really can't handle well.

Some examples:

Economy and morale:
AI seems to get trapped into a raise taxes, build morale buildings loop. While I usually customize my races with a morale bonus, I don't think 7 Entertainment Networks are needed on a farmless planet if one doesn't have a morale ability.

Defense:
When I want to attack a new enemy, I usually do the following:
- Send a scout to check what weapons enemy has
- If needed, research defense
- Mobilize fleets near border, save some money
- Design new ship model with appropriate defense, upgrade existing ships
- Get fleets into strategic positions and launch an attack

The result is that my fleets barely get scratched while I decimate the enemy. The AI never manages to get the proper defenses against me.

Offense:
AI should position fleets prior to declaring war on a player. There's no point in a war if there are no fleets to attack. The AI needs to take players by suprise.
Usually I leave all my planets undefended with just a few fleets at the border of my empire. I can just intercept most of the enemy fleets coming at me.
If AI would preposition their fleets, I would have to use defenders or to do preemtive strikes. (Get off my lawn ya transports!).

The end result is that I can conquer the entire galaxy with only a handful of fleets without any real resistance.