The smartest thing I've seen the AI do is surrender to me.
The next smartest thing is targeting my weak planets where no ships are defending with a transport, and surprisingly with a few escorts to protect them on "intelligent". The other smart thing they've done is place influence bases near my weak colonies. The one who does this first is my first target for war.
I was getting too confident and thought I could go all offense. I was relying on backtracking with a few defending destroyers in case of attack. I figured their slow speed would give me ample time to intercept but they went through the one section I didn't have a base to screen. So they aren't that dumb but they can have their good and bad moments.
The best thing they do is go around your military bases once in a while.
Biggest Problems with A.I. at this time:
1. Speed. They never place any speed on their ships. They should have attacking and defending ships like someone pointed out. At least place the engines on the attacking ships and if they are going to do a surprise landing "always" send many escorts to protect the troops.
2. They never seem to research anti-missile tech so I always go missile for easy kills. They always seem to go with lasers and I have either traded or researched for the shield techs to counter them.
3. They always put laser guns on their base which I again counter with shields. I think they should put the weapon type that suits the defense weakness of the neighbor nearest the base. So if to the bottom the Thalans have no defense to missiles they should put missiles instead of lasers. If they know that everyone has shields why do they put laser tech instead of mass drivers or missiles. They should know since I've been trading it to everyone. They can see in trading as well, or should have access to any information I can access for free as well.
4. They don't seem to use enough military bases for defense and ship support or as a preemptive maneuver; placing a military base to extend influence into an area where they have plans to attack later. I do this but they don't do it, or I haven't seen them do it yet. They don't prepare attacks like this or try large assaults on one weak point.
5. Trading tech they should try to keep as an advantage to themselves. I do this with missile techs so I can gain an advantage but they don't do this at all. Unrestricted tech trading has ruined the game for me. If it remains unfixed I will lose interest pretty soon I think. I'm already tiring of having to tech trade every 2 or 3 rounds just to keep up and control the tech trade so I don't get left behind. I can't play my xenophobic research style anymore. This is a bigger problem than all combined in my opinion. You can easily become the guy that everyone gets their tech from, and control the game, while all the enemies become the same enemy essentially. The game is heavily unbalanced to favor aggressive expansionist diplomats.
6. They seem to favor offense over defense all the time even for defending ships. I follow the rule defense before offense. Follow this rule and keep your high defense low offense ships in a fleet. Pick out small targets till their HP gets high and then they will become unstoppable. They should try it out.
The game has a huge potential that awaits to be realized.