Well I just finished up my first game for the beta of Elemental: Fallen Enchantress. Actually, I didn't finish it, because my game crashed and now none of my three saved games will load. 
Anyway, I was on turn 600-ish of a Large map, normal difficulty with max players (12, I think?), and was pretty much dominating the AI with little effort. I had around 1000 score, while the next highest was 200 or so.
First off, I think it's important to inform you guys that ever since my very first crash, subsequent crashes have not been generating dump files anymore. I have tried renaming and even removing the old dump files and nothing seems to work. I no longer get crash dumps.
Second, here is a link to my save file, if it will help identify any issues. It crashes for me every time I try to load it.
http://www.box.com/s/5201ikqu1xe2t609vd21
While I was playing, I kept a little Notepad open where I wrote down anything that came up that seemed to be bugs or issues, and here are those:
BUGS
Tactical Combat - Mounted AI units, or any unit with a large number of movement points seem to not attack most of the time, even if they move adjacent to one of my units.
Tactical Combat - Tangled Web doesn't seem to actually do anything. It claims the target is immobilized for 3 rounds, but it seems to have no actual effect.
The item Gauntlets of Grazna claim to increase both defense and strength in the description. They do not increase strength.
Building a Crystal Foundry or Iron Ore Mine doesn't cost any gildar. Actually it seems like most buildings have no cost to build it other than time. Is this intentional?
You can still click to build on resources outside of your territory, and it actually changes the icon so it looks like you are building something, but once the next turn comes, it will be back to normal.
Sometimes there is no sound in tactical battles.
Searching a Lost Library gives the message: "Found Ancient Texts - Searching through the ruins you find several ancient texts that hold important knowledge from the past!" But this doesn't seem to actually do anything.
The Head of Torax city trophy obtained from the desert wildlands claims that it adds +10% to taxes and growth, but actually -subtracts- 100% from taxes. Not a good reward. 
AI Impressions:
AI doesn't do a good job recruiting champions. I captured multiple AI cities with one or more champions practically right next to the city walls. I also noticed it seems like Kingdom AIs in particular were ignoring champions.
AI does a terrible job protecting their champions and using them effectively. AI Champions that had died many many times were a very common sight throughout my game.
http://img38.imageshack.us/img38/8284/fe002.png
http://img252.imageshack.us/img252/4919/fe003.png
As well, AI champions were -way- behind mine in level. I had four champions over level 20 while the AI had none above level 10, most of them were under level 6
Tactical Combat - The AI -never- waits for you to advance so it can get the first shot on you, even if it has ranged attacks. If the AI has a lot of archers, and their enemy has no ranged attackers, their melee troops should really be staying back and forcing the enemy to come to them while the archers pepper them with arrows, then their melee can get the first attack on units already weakened by archer fire.
Tactical Combat - The AI has a tendency to move caster units, even if extremely damaged, right up to my army. On multiple occasions I saw the AI move a mounted caster unit with 2 hp right up to my army, and then cast Obscuring Fog defensive spell.
UI Comments:
Mass Curse really doesn't need a skull over every model in the unit. It clutters the screen quite a bit.
http://img853.imageshack.us/img853/286/fe001.png
Gameplay Comments:
Did the Arena quest. The obstacles on the battlefield there would make for an interesting layout. Would be cool if FE could use rocks/fallen trees on regular battlefields like Heroes of Might and Magic does. However, it appeared that units could walk right through all the obstacles in the arena battlefield, so that would need to be fixed.
When your units are defeated in battle and retreat there should be some scaling in the amount of mana they use. I had a practically useless level 4 champion die and use 624 mana to retreat. Would've rather just lost the champion. 
Balance Comments:
It's hard to comment on balance when I can't play against another human player or even against myself to test things out. As it is, everything I tried, whether it be a magic heavy army, or a pure physical combat army, completely trounced the AI since they seemed to make no effort to counter any of my strategies. (If counters even exist. I don't really know, since I haven't had to worry about countering anything the AI has done so far.) The only comment I really have is it seems like defensive gear/spells/traits/abilities are underpowered and much harder to come by than offensive gear/spells/traits/abilities which results in a lot of one shot kills in combat.
For instance, let's look at the first tier of weapons and armor that you get.
For 60 gildar you can get an axe, which is +1 crit chance, and +10 attack.
A whole set of leather gear and a wooden shield will get you 9 defense and 2 dodge, but costs a ridiculous 720 gildar to get it all.
Similarly with troop design, an axe has 10 labor cost, and 2 iron.
A full set of leather armor and wooden shield has a 37 labor cost.
Of course the upkeep costs of having three to four unarmored units against one armored unit might balance this out, I don't really know at this point, since I've only played through one game so far.
I haven't read through the forums a whole lot, but I notice multiple threads about champions being overpowered. This may be true, however I think the weakness of the AI and it's lack of ability to utilize its own champions effectively is amplifying this a lot. Against a human player with similarly levelled and geared champions, things would be much more interesting. Have you guys considered adding multiplayer to the game?