Great job! I definitely agree with Gabe about the minimalism and how well you've used the one button theme.
The point made about the difference in speed between the web version and the download is interesting, I assume the game speed is tied to framerate at the moment so making it independent one way or another would definitely help.
As for other technical issues I noticed that if you move your block into the middle of one of the yellow enemies as opposed to hitting the head, then the block would not visually reset back to the beginning until your next move, which leads to the block updating backwards at times, potentially hitting an enemy again and looping the whole issue. I don't think I can really suggest a fix for that without knowing why it's happening in the first place unfortunately.
Also, you can move the block off the end of the level and float into the void, the level will still complete once both blocks have moved onto / past the end zone so you don't get stuck, but it still looks a bit funny.
As far as design is concerned my only minor feedback is that a couple of the levels are functionally identical on both sides, which I feel is a waste of the flip mechanic. Again, only a minor issue but maybe having more objects akin to the buttons and walls would help differentiate between the sides a bit more.
And finally on a minor visual note I think it would look nicer if the grid was only visible on the game board and not over the whole screen.
Sorry if I come across as too negative, the actual idea of the game is great fun!