One game of several hours under my belt, and here's my list of encountered issues. Most of these are not gamekillers, but they should be addressed. (Sorry this is a pretty big post but I'd feel like a tool making a new thread for every single one of these, especially since many are UI issues.)
Overall, I had very few appcrash events, which was refreshing for a beta, but an alarmingly high number of apphang events - nearly all associated in some way or another with the beginning of my turn. I had autosave set to every turn and I believe the majority of the hangs were occurring at or before that.
[BUG]: Each obtained 'vendor trash' item from a battle is reported individually. If I get two Spider's Silks, I really should only need to get the notification once - especially since I can see the item count during the results screen. (Wolf Pelts are not reported at all, incidentally.)
[BUG]: Fireball spell (and probably other related ones) appears as a unit in the tactical queue, indicating that the spell is ready to be cast. This is great, until in between preparing the spell and casting it all the available targets either die or move in between my units, leaving me with no valid targettable squares - and no way to remove the fireball from the tactical queue. The only way to continue the battle is with the autoresolve button. There should probably be a way to cancel out of fireball and similar spells.
[BUG]: I can see what an enemy town is producing as well as population count, even with no treaty. I'm unsure if this is working as intended. Seems unlikely.
[BUG]: Even though the "Build" button is grayed out, I can still click on it to build buildings on resources outside my influence. The buildings go away after a while, but I still get vision on the squares adjacent to the resources. Vision is also occasionally granted around some resources or points of interest at random times for random durations.
[UI BUG]: In the Unit Details window for Sovereigns and Champions, mouseover tooltip for traits does not update if mouse is moved from one trait to the next, as it does for regular units. Mouse must be moved away from the row of icons to dismiss tooltip before a new one can be displayed. This only affects Player-owned Sovereigns and Champions - AI-controlled Champions have proper tooltip functionality.
[UI BUG]: 'Defend' visual effect is not removed during tactical battles after it expires. If a unit is moved under effects of Defend, a second sprite is created at the target tile, which is also not removed. It also takes several seconds to load the sprite, a very drastic delay compared with all other spell and skill effects. This may affect other skills as well.
[GRAPHICAL ERROR]: Tiny little thing, but it bothers me. The left arrow on the pose selector when making sovereigns and custom units appears behind the row of silhouettes, making it hard to both see and click on.
[GLITCH]: It is possible while in build mode overview to scroll the map to another town and select it to enter build mode without ever exiting build mode from the first town. This causes the highly desirable 'return to previous camera position' functionality to be overwritten with the build mode angle. I very much like being able to scroll from city to city in this way, I'd just like to have the 'exit build mode' button revert to the camera position I had before starting it. Perhaps navigation buttons to scroll between cities while maintaining build mode?
[REQUEST]: Give us a notification, maybe on the HP or Constitution tooltip, to see how much a unit is going to heal per turn.
[REQUEST]: I finished the quest of mastery, and because of previous experience with WoM I knew it was coming, but there was no real ingame indication that things were about to end after I fought the final battle. Knowing that I'm on the path to victory would have changed a lot about my game. I'd also love to have the option to complete the quest with the victory condition turned off, so I could play with the fun things and XP I earned in the fight. (Oh yay, a popup informing me that I got a steel mace... over the endgame screen. Might want to look into that.)
[REQUEST]: Allow us to assign a 'spawn point' for cities that do not automatically garrison created units. It's nice that units appear in a consistent location, but I really don't need my frontline troops spawning in a dead-end box canyon behind my city. This should be distinct from the genre standard "rally to" point that is also unavailable.
RELATED: I had a border city that was constantly being harassed by enemy troops. With my sovereign on the other side of the map, I didn't want to bother with fighting a two-front war, so every time a stack of units showed up in my territory I just nuked them with the fire spell that leaves an inferno. A few turns later, I had a guard unit stationed in the city and sent it out to harass a passing caravan. It spawned in the inferno (I tried this more than once, every unit I sent in that general direction stepped out into the flames), went to 2 hp and was teleported to just off the very bottom left corner of the map (with no indication of what had happened). That's a whole suite of bugs and AI changes that could use some TLC.

That's where my screen goes when I click on the immolated unit.
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Ok, I'm new at reporting beta issues so don't hate me too much, but here comes a horde of visual issues:

Icons for Prodigy and Prodigy II are incorrect.

Typo and grammar error in Skath Fin text.

Tooltip error.

Related: Champion riding Ravenous Harridan does not appear at all in portrait. (Also, Non-Player Character Player?)

I guess this means we can haggle hiring costs with some champions? No indication how much it cost me to hire this guy, fortunately I had plenty of cash.

So by the name and that next-to-last sentence in the flavor text it would appear this is supposed to be a female champion... hi there, beard. Other notes on this one: flavor text says he's a healer, but lacks healer trait. Says he has a mace - check, I can see that. Says he has an amulet... well it's not visible but the champion did have an amulet equipped when I hired him.
That's a lot of little nitpicky things, and I have to say I'm incredibly pleased that the worst complaints I have about the game are tiny issues like these. Overall it looks amazing and I'm really excited to see the final product!