I started a new game

3 Empire AIs
2 Kingdom AIs 

Small Map
Expert difficulty
Moderate monsters
Dense magic
Dense resources 

Sovereign:

Altar

Life Apprentice
Earth Apprentice
Wealthy
Brilliant
Vuln. to Magic
Procipinee's Crown 

And saved the game every 5 turns.  At the end, I went back and used crtl-u to see what the AI was doing.  Comments below.

Bugs

AI Oddities / Potential Improvements
(Note - Brad probably has a lot of these on his to-do list, but I'm just noting odd things I saw the AI do)

AI should prioritize lost libraries, especially early when they're 4-5 turns of research
Doesn't build enough outposts to claim undefended nearby resources (people say they expand too fast?  I've never, ever seen that in Beta 4)
Prioritize resource improvements towards things that are useful early.  E.g. build altars before crystal mines
Be smarter about placing outposts to maximize the amount of resources they contain and minimize the number of difficult creature lairs they'll cover
Reevaluate the placement of outposts and cities once it gets to the path-to location to see if anything has changed (aka someone building a city right next to where it wanted to build an outpost)
 

Turn 5

Procipinee's city only has one essence, she cast inspiration.  That's probably a good choice.

Yithril's city has 3 essence, he cast Hammers and Inspiration.  Both good choices, but he can also cast sovereign's call - why not cast that also?  25 mana, yes, but it's turn 5.  To be followed.

Gilden's city has 2 essence, he cast Hammers and Inspiration.  Both good.

Magnar has a 5/3/3 with Sov's call and Inspiration.  Has not yet recruited his first champion either, but has a sand golem.

Resoln - as Procipinee, on a 5/3/1 with inspiration.

Also of interest - somel AI sovereigns are adventuring with their first hero and losing xp because of it.  

All are building pioneers, but Procipinee's 5/2/1 without Hammers is going to gimp her badly

Turn 10

Procipinee & Resoln are still working on that first pioneer.  The 5/2/1 start without Enchanted Hammers is a real problem.

Yithril cast that 3rd enchant, built a pioneer that is being escorted somewhere, and is now building a crystal mine.  

Gilden has built a pioneer that is being escorted somewhere

Magnar is about to finish the first pioneer

Turn 15

Checking up on the sovereign / champion progression - it's much improved from the past when the AI would be way behind the player.  

My sov is level 4, champion is level 3
Magnar is still solo, but is almost level 4 
Gilden's sov is level 4, champion is level 3 
Procipinee is 3, champion is 2 (teamed) 
Yithril is 3, champion is 3 (teamed) 
Resoln is 3, champion is 3 (teamed)  

No AI's have founded their second city.  Magnar chose to use his pioneer to create an outpost in a sub-optimal location.  To avoid angering some wolves that he could have slaughtered (he was 3-4 turns away), he skipped a shard.

Procipinee finally finished the pioneer

Turn 20

Procipinee's first pioneer reached the location and found Gilden had gotten there first.  Instead of moving somewhere else, the pioneer plopped an outpost 2 squares from the city.  That's like giving Gilden the outpost.  (Gilden got there about 2 turns before Pariden)

Procipinee's working on a second pioneer and it's turn 20.  Nothing else has been built.

Resoln has had a lost library next to its capitol for 20 turns now and has ignored it

Yithril is cranking through, with a scout, a second city, and another pioneer.

Gilden and Resoln both placed outposts in intelligent locations.

Turn 32

Procipinee built another 2 pioneers.  One settled the square next to the city:  She got some great resources, but a monument would probably have been more cost effective at getting them

Magnar placed an outpost over a Fell Dragon lair.  Interesting to note though - in the actual game, that Fell Dragon did not move at all for over 30 turns until my units spotted him.  Then they were chased and the dragon went wandering.  Also interesting - when I ctrl-u to see everything, the dragon would then chase the AIs.  But, until I revealed the dragon, it was completely inert.

Turn 50

Checking up on the sovereign / champion progression again - AI's are still doing very well with keeping up / beating me, though I'm largely out of monsters on my corner of the map.

Me: 7/6/4
Magnar 6/2
Gilden's 7/3
Procipinee 7/5
Yithril 7/6/5/3
Resoln 7/7/7/6

At turn 50, here's the world map:

Note the large areas around AI cities that are not claimed by outposts but have resources.

• On the middle left are 2 crystal mines that Pariden refuses to claim with one outpost, and a death shard and a clay pit that could be claimed by another, and an earth shard / crystal mine that could be claimed with a 3rd.  But Pariden is production gimped (20 prod at turn 50), so maybe that's it.  
• Just up-and right of center are Twilight Bees and Iron Ore, undefended, right by Magnar, who wasn't afraid to build over a Fell dragon
• Barely visible on the far right is an air shard and wargs.  They're lightly defended, bu Resoln has 3 champions that could clear the area out.

Fast forward to turn 75

Pariden placed an outpost in a terrible position to just claim one of the crystal mines.  None of the other resources near there have been claimed by anyone despite the lack of defenders.  

By turn 100, about half of them were claimed.  But the area on the north-east, now cleared of monsters, had 5 unclaimed, undefended resources.  I keep seeing people say pioneer spam is a problem - everything I've seen says the reverse is true - the AI has pulled so far back on pioneer spam that it now refuses to settle areas.  Some tuning is needed (and is probably planned) to a balance.