First off, this is a great improvement to the game; you've still not approached the final potential, but it's become a lot more fun to play. Still waiting for it to graduate to awesome, though:-p Here goes:
1. prestige in cities is not updated when heroes enter; I had my sovereign in my capital at the beginning but only had my base prestige. Upon building the beacon of hope, it went from the base 2 (I chose royalty) to 6, so I think it triggered the calculation at that point. Obviously the displayed amount should change immediately, and what you have on turn start is what matters for population growth.
2. Rilis is one of my favorite to recruit - I was very excited to finally be able to use her 'Crushing blow' (unblockable max damage hit, usable 1x per 3 turns). While the animation and such looks correct, and claims that the max damage is done, if you check the actual health, it looks like it did a normal attack with variable damage (by definition less damage than claimed).
3. your underpinnings are showing:-p That is, I had the same problem as  with at least 1 spell (fireball, I think); it claims a specific damage in both the spell text and the graphical smackdown, but considerably less was done to the target (by underpinnings showing, I mean that special abilities are handled by the same code as the spells, shows again in )
UPDATE: just cast burning hands against a bandit; claimed 8 damage in the graphic, did 0.
4. Rilis did a crushing blow to a darkling. The darkling was immune?!? Awesome that magic immunity finally works, but a physical talent is a separate concept from magic, so this is jarring and probably a bug.
5. Every patch I keep expecting the mine flavor text to be fixed, but I guess no one has pointed it out - 'weaopns', I think.
6. I did battle with Umber; their typical City Guard troops ALL resisted not only my spell blast, but every other spell I cast (fire spells, 1 shard). Not a problem with the beasts of the wild, I suspect a problem with the troop generation code. NOTE: this wasn't a single battle bug, it happened at least 2 combats (during the 2nd battle my computer slowed to a crawl and then crashed out of Elemental when I Alt-tabbed out and back in, which is when I decided to write up my thoughts:-p)
7. There's a spell that claims to do 75% of damage, but the calculated amount in the text below is much less; more like 25% (1-% error, maybe?)
8. I often use the number pad to move; while this only works well in zoomed out map mode, it is the quickest and most precise way to move, so I like it The problem is, I can 'skate' across the entire continent in 1 turn - by simply pressing my next move at a certain point in the move animation, I never use up any movement points. I know this used to be a problem with clicking as well and you patched that, but it still exists with the number pad.
9. the text alignment of the number-based details (at the bottom) is goofy for several spells
UPDATE (a few items I forget):
10. spoils of war: turns into a growing list after the first battle (post load or save); seems to be a list of previous rewards? It's selectable, but I don't know if that has any effect on what you're actually given. It's also sorted, but that may be because you have larger amounts each time (would indicate that you're getting the sum of the list)
11. Defending a city / Guardian Defender: I took a city from Umber, and they have attacked several times to get it back. There is no noticeable defense, either in battlefield or stats. The walls a a nice graphical effect on the overland map, though.
Missing / falling short:
1. There is no single active magic list, nor explanation of current usage. Kind of critical now that you have global upkeep for spells, there is a big gaping capability hole there. I expected something along these lines when I clicked the mana up above, but no dice - it was the city screen instead (I *love* the city screen, btw - it's just not appropriate if I'm looking for information on mana generation and usage, which I would be if I clicked on the mana section of the resources bar).
2. You've attempted to simplify the hero/unit display, but you went too far - most especially because you've removed intelligence. Not only don't I know if a hero is a good potential caster, I can't check how far they are from being able to cast a given spell. Moral of the story: if a stat is transparently required to do a given action, it should be visible.
3. the idle city popup is a good start; can we get an option to 'go to city'? Would not be effective when multiple idle cities pop up at the same time, but I generally need to see my city's situation before I know what I want to do there.
1. is it intentional that the familiar is a caster?
Summary: Clearly you weren't kidding that it's a beta, and it is also an awesome improvement for the game. Rock on!