I really like LH. "Time Played" is 163:07! I've spent the past 3 days on one game, and am only about halfway thru it. Game is huge world, insane AI, 5 insane AI foes (all empires, I'm a custom kingdom). Settings are mucho resources and magic, no wildlands, temperate. Currently turn 264 and I'm (Dangerites is me) hanging in there...

The game is beautiful -- the art is lovingly crafted. We can easily tell which element a shard is, and if it's developed. We can see what weapon our Sov is wielding -- not just on the paperdoll but on their tactical representation. We can zoom in and see the people doing their daily tasks.
Balance is constantly improving. Spells are interesting. Exploring is fun. All in all a lot of good stuff, and a good game.
The one part lagging behind the rest is the AI. It's not that the AI is terrible, it's that the rest of the game is so good. There's no MP, so the AI is all we have. And it's a strategy game. And we've heard how the AI will make us cry in anguish it'll be that good. I have suggestions to make that claim more a reality, all based upon my insane AI world and insane AI foes observations in many hours and multiple games, and with the clarification that I'm an average skill player (in Civ4 emperor difficulty is a challenge for me) so insane difficulty should be beyond my ken:
First tactical:
-target selection. The AI needs to better select the most 'dangerous' target. Suggestions to prioritize are ranged, Sov, champion, nearest melee (nearest in terms of # of moves to close to melee attack range). Within each 'category' the unit capable of doing the most damage comes first (so amongst ranged units, an 'ice' mage would come before a 'fire' mage if the targets are immune to fire attacks).
This can be modified based upon the AI leader/race. For example, a 'mage' AI sov might fear melee more than magic so melee would be prioritized. Or maybe a 'mage' Sov would most hate the 'competition' so would prioritize magic foes. This provides a means of making the AI sovs more unique.
-focus fire. I've seen one good example of focus fire in my current insane AI game -- the fire skeletons at the end of the 'night of the skeletons' event focus fired at one of my units despite my best efforts to save him (moved him back, moved other units nearer the fire skeletons, etc.). Every other battle it appears that the AI randomly and individually select their targets with no regard for finishing off wounded units. In one battle of my 6 units vs. 6 shrills I should have been wiped out but instead I won with no deaths because the shrills appeared to do everything they could to not kill any of my units. A unit with only a couple of health remaining was adjacent to 2 enemy units for several turns and they instead attacked distant units. No way that unit should have survived.
-moving to maximize attacks. When I move to engage I try to maximize the number of units I can get adjacent to the enemy. I'll also move after engaging if it'll help add in another unit to the attack next turn. AI doesn't do this, it'll just sit there with no regard for adding in more attackers next turn.
-target selection. Example -- AI unit #1 is adjacent to 2 of my units. One of my units has 2 AI adjacent (so swarm=2), the other has 3 AI adjacent (so swarm=3). All else equal (and in this case all else was equal) the AI unit #1 should attack my 'swarm=3' unit but instead it attacked my 'swarm=2' unit.
Strategic
-preparing before declaring. Been mentioned many times for many versions -- the AI should prepare to attack before attacking. Create armies designed to counter the target's units, preposition the armies, then attack.
-spells. I've never seen the AI cast freeze/tremor or similar spells on my armies in their territory. I've never had any AI cast damaging spells on my armies that can be cast out of the AI's territory. I've never seen an AI couldwalk in to defend against my incursions. I've only seen 2 or possibly 3 spells cast on my cities (and I pay attention to this) in all my games, most of which were on ridiculous and now insane difficulty.
-I'm still seeing cities with no production. Could it be a 'figment' of a unit being produced and no second unit queued for the 'in-between' turn and there will be a unit queued at the start of the next turn? or is it a true 'no production'?

-I'm still seeing AI create units in non-fortresses. I specialize my cities -- my capital is usually my fortress, with all the unit augmenting buildings/spells, and this city creates all my units (until I can add in a second such specialized city) as much as possible, units with all the combat bonuses I can pack in (I then try to keep the units alive -- quality over quantity).
-I'm still seeing AI armies sitting still for several turns (not as long as in the past where a unit may sit for 50 or so turns).
-I'm still seeing unclaimed goody huts in AI territory (someone suggested after I mentioned this months ago it was 'strategy' but Frog or someone mentioned that if an AI passed thru an unclaimed goody hut without specifically targeting it the hut would not be claimed, and this appears to still occur).
-reforming armies. I cast tornado, AI stack is scattered, and most of the units just sit there. A few will move, but none will recombine.
-coordinating armies. I'm seeing multiple stacks approach, I'm not seeing them coordinate attacks effectively to wear me down and overwhelm me.
-army composition. I'm no longer seeing pioneers in armies, but I would like to see units specifically created to counter the target's strengths/weaknesses. And better composition regarding melee and ranged, augmented with champion spellcasters (combined arms).
-diplomacy. An AI offers me a tech trade -- wants 1219 gildar, I have 171 gildar and am netting 2.2/turn.
There's more for both tactical and strategic, but that's all I can think off off-hand... There's a myriad of threads with other points, such as the one on settlable spots, etc.
I mentioned AI needing work in another thread and the response was:
1- some folks 'abuse' CTL-N for a great starting location and custom Sov creation to 'beat' the AI
2- the response to improve the AI could be to increase the bonus modifiers (AI units are bigger/sooner)
Regarding 1, as I detail above, there's a lot of room for improvement. I'm not talking about Einstein AI improvements, but basic ones like 'focus fire' and 'target selection' and 'occasionally using the spells provided'. It's not CTL-N beating insane AI, it's the lack of 'intelligence' in AI.
Regarding 2, this is the easy way out. Anyone can increase a modifier, or nerf and/or remove spells/abilities. Adding intelligence to AI is hard, but we have no MP, and we've heard claims the AI will be good. Increasing modifiers doesn't make the AI better.
If the AI remains as is, LH will still be a good game. Given the skill of the team working on the game it'll just be a lost opportunity to advance the genre (I'd be happy if it would match Civ4's AI...).
Edited in:
Remember, the above is based upon insane world/AI difficulty. For lesser difficulty levels the above may not apply. For example, with regard to focus fire -- on the easiest levels avoid focus fire, on the middle levels make it purely random (it happens occasionally), on higher levels it should happen all the time. This way difficulty is based more on intelligence and less on bonus modifiers.