In the last few days I've had a try at the demo, and I quite like the game. Being a Lemmings player it took me a while getting used to the differences, so please forgive me using Lemmings terminology in some instances.
The Quantum level confused my a bit at first as to how that system works, but the level in itself was very fun.
I also missed the notion at first that the clones lose value over the time in DrillDude's level, but the latter is my fault, as it's quite well stated in the bubble in the top part of the level. I really like this new type of level; optimizing time for every single clone is something I haven't encountered previously.
Another thing that took me a while to realize was that the upward and downward miners are shared.
Apart from the ice level, which was already stated to be quite a bit buggy, I didn't really find any major bugs (apart from the known occasional crashes during multiplayer and the incompatibility of the Quantum level replays causing crashes as well).
Only two rather obscure ones:
If there's a one pixel thin layer of terrain, the clones will walk on it, however if you try to start building, they immediately stop after the first brick.
There seems to be some delay after the start of the level, or after un-pausing, before you can pause again. Not sure whether that's intentional.
I'm not sure whether the issue of the wrong skill getting assigned during multiplayer still holds; I suspect it might have been the skill selection belt that I clicked a split second before pressing the key. I disabled it, and encountered a mis-selection only once today, and perhaps I just hit the wrong key there.
Some of the problems in the ice level have already been stated, but here are some more I encountered:
I suspect you're supposed to save one of yours as well as the white clone, which should make this level work without issues, but if you're trying to get more than one green clone up, it seems that trouble ensures (which prevented me from completing the level for a while). If a clone enters the exit or splats (as opposed to e.g. drowing, getting sucked by a black hole or getting electrocuted), your view doesn't autoselect a new clone, and also doesn't perform some essential updates, like creating the shortcut teleporters, resetting the vanishing blocks or making the moving objects move again. So if for example you saved your first clone, but not the white one, you're pretty much stuck as the teleporters to the top aren't created, and the objects stand still (and you don't have an ascender anymore either).
There was also one instance where a checkpoint returned me to a wrong state. I think it was after using a user-checkpoint, but then restarting from the auto-checkpoint and overwriting the user-checkpoint with a new one. Loading the user checkpoint just loaded the auto-checkpoint again. In fact, I just re-tried, and upon setting and loading a user-checkpoint after having passed the auto-checkpoint, the wall which dissolves when hitting the auto-checkpoint was still there, with both clones still in there (one being auto-selected). I took one and mined out of that wall to hit the checkpoint again, which caused the wall to dissolve and two new clones appear there, both of which were uncontrollable and just walking around aimlessly.
It's possible to get stuck in the corner of the rotating L-Blocks, so you're safe even though you should fall into the water. In fact, if you keep pressing a directional key, you can even sift upwards through the L block and end up on its top. I suspect this is caused by the physics allowing to stand on arbirarily high angles (e.g. you can stand on the left one of the vertical edges of the rotating square blocks further right in the level).
I also managed to get stuck between the steel blocks in the section with the black holes once, but usually I seem to get out between them.
Another issue I had was the just key reacting delayed (or not at all, I don't know), when trying to jump off the dissolving blocks. Might have been that I've been pressing (and holding) the key slightly before landing though, so I don't know whether this is really an issue.
Some observations on the multiplayer aspect:
The multiplayer mode is really fun to play, the clones move a bit slower than Lemmings, so your gladly reaction doesn't have to be as quick. It's still easy to get lost in the game.
A tendency we noticed already in Lemmings, but which is also prevalent here is that blockers, and to some extend also drillers are very powerful in multiplayer. Blockers block the way instantly, and are very hard (or impossible if standing one steel) to remove for the opponent. If the ceiling above them is solid as well (e.g. in a basher tunnel), then it is very difficult to build over them as well. (In Lemmings++ this lead to the convention to make blocker-less/sparse levels, even though they are less powerful there as they get blown back if you launch a bomber nearby. They frequently caused blocker-battles near the exits, which weren't overly fun.) Drillers are very fast, and pretty much catch surrounding clones in their tunnel. The atomizers allow to counter that to some extend, but bashing and re-drilling again seems to keep the drillers at the long end still.
If my mind serves me right, I think the steel blocks in the 8P level are a bit misplaced so that it is still possible to create a deadly drop under some entrances by removing the terrain there.