Hmmm... Lemme see what I can find in there...
PART 1 - Thief turorialNice music ! And no doubt, you've managed to make things much more lively than in the first game. What probably plays a big role there is that you have added lots of random moving background elements (flags, birds, the stone oscillates slowly as the Thief reaches it, even lights do not have a constant intensity...). Speaking of the background, I'm curious : this cannot be rendered in real time while still running on a modest machine, right ? And yet you have this pretty parallax effect around. Do you use several layers of pre-rendered content or something ?
Also, the physicist in me loves the work on lighting, including the scattering of moonlight next to the edge of buildings in the background. More generally, lots of pretty lights around, it's just a shame that video quality is not good enough for me to have a deeper look at this.
It's still pretty obvious that the thief's animations are pre-rendered, though, and ropes still disappear when cut, but I also bet that I still won't notice this much ingame.
PART 2 - Warrior tutorialMore moving background elements, and pretty background lighting, although I wonder if it's not a bit too powerful. Also, I see you've worked a lot on colors, as the contrast between this part and the previous one is striking. Also, nice swordfighting animations !
Again, the world has more depth, but this time also because of foreground elements, which is more unusual but looks just as good.
PART 3 - Between a (big) rock and a hard placeMore colors and lights ! The pushing animation and the way the stone block loses equilibrium and fall look better than previously, IMO, and I love how the goblin (let's call it this way atm) suddenly looks upwards and screams one fraction of second before being crushed (who said that video games are the place where I express my natural cruelty ?

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PART 4 - Watering the plantYay, fluid mechanics and refraction ! One big problem which I have, though, is that I can't see how water can flow without leaking on the wizard's plank, which is after all full of holes with all its cogs.
Should I want to nitpick, I'd add that the point where the flowing water meets the plank is not very realistic : the water flow should be thinner at this point, there probably also should be some splashing on the foreground and background of the plank, and a bit of water should flow in the opposite direction, at least according to my experiment with the kitchen's faucet and a ruler. Also, around 0:40 and 0:42, when the wizard moves the plank a bit forward you have a great example of hitbox disaster : water is deflected by... err... nothing. Notice how the person who shot the trailer quickly takes the plank back on the left when noticing it. Oh, well, I prefer this over hitboxes which are too small, making you miss objects when you jump on them

Speaking of jumping, can we now grab the edge of platforms when reaching it while falling and then climb on top the Rayman way, at least with some characters ?
The water itself is pretty neat-looking, and I love how it splashes around a bit when hit by objects or the Wizard itself. Wizard character animations are great and magical effects are also very nice, although I suspect that they could maybe look as great on my PC in Trine 1 if I could set graphics settings a bit higher.
PART 5 - Thief awesomenessWell, the title says it all. This is the kind of fast-paced, acrobatic gameplay which makes the Thief so fun to play in some places. But how exactly did she kill the first goblin ? Does she have a knife or is it just a big kick in an area where it hurts ?
PART 6 - SpidersNOOOOOO !!! NOT THEM AGAIN !!! Well, at least it sounds like although they have become tougher, they have lost their ability to fire an infinite amount of rounds at insane rates.
Also, yet again another big background change to picture the bigger contrast between levels in Trine 2, and monster animation is awesome.
PART 7 - Basic wizardryWell, some classical puzzle-solving of the Trine world, the interest of this part imo is to showcase the new funny animations of the Wizard.
PART 8 - Funky plant and the ForceI love the ability to grab creatures with the Wizard, it reminds me of some of the most awesome Star Wars games ! Will this be doable with every creature, including for purposes of making them fall in a pit or dropping them from high, high above ? Will this work with players ? Is all this supa-secret information ?
Also, good use of the third dimension. I love this idea of something coming to eat you from behind... It's like the swinging blades of Trine 1, only more dynamic.
PART 9 - The snailA pretty snail which pretty much sums up the "200% more rainbows" side of Trine 2, the increased use of the third dimension, and the new puzzle elements

I wonder, though : will all plants which can be watered be noticeable through such little sparkles, or will some be hidden ?