I think you could do with smaller levels. There's a lot of empty space which is there to make you walk around rather than because the space is required for a puzzle. Walking is not fun: try making each level as small as possible (
ref: level design workshop exercise 1). This problem was particularly pronounced in the introductory levels: every outside level could have been a single non-scrolling screen without losing anything.
I think you should add new gameplay elements more slowly and focus more on the puzzles. There aren't any actually interesting puzzles until level 11 or so, before that it is all simplest-possible-puzzle for each new item. That is not fun in of itself!
Movement is slow and feels a bit unresponsive. I think it's possible for key-presses to be lost if you're moving when it's pressed?
"You are an adventurer": don't say this, it's obvious anyway but it also breaks immersion and just isn't good writing (i.e. show don't tell).
Level 10: blocks on top of fire should have some visible indicator that they're on top of fire! I agree this level is too long. All of Increpare's comments on this level are spot-on, it's too long and there's too many places where you can die after encountering a new mechanic: forcing you to replay the whole level again. The message "Lava requires both fire and water protection" has never been so annoying...
The behaviour is unexpected when you move onto ice without there being normal floor across from you. I expected to be stopped by the wall and then to be able to choose a new direction to walk in, instead I bounce back. Not really a problem I guess, just something I thought was a bit weird. I also find it weird that a wood block pushed on top of water doesn't react (I'd expect it to create a walkable platform).
I am not sure how much some of the enemies add to the game but maybe that's just me being a puzzle purist. Since it is a tile-based game, avoiding enemies early on is just been about timing and isn't particularly interesting or skillful (note that "oh crap I have a very short time to press this button or I'll die and have to restart the whole level" does not require skill, it just creates frustration). Some enemies like that rat have puzzle implications that work fine so possibly it is just a few enemies that aren't necessary.
Overall conclusion: it's certainly a promising set of building blocks for puzzles, as I said before I think the puzzles themselves could be streamlined though.
Sound-delay: Linux has an unavoidable half-second delay on every sound. If Increpare is having issues not on Linux not sure why that might be: that code snippet looks fine.
I think I remember hearing something like "each time you play a sound for the first time in a scene (or something) flash has to start up the audio subsystem".
I
think this was a problem with older Flash players and shouldn't be an issue with AS3. Could be wrong though.