I like it. Some thoughts as per request:
- Give us some scores, achievements, medals. E.g. give scores based on time needed to solve and give a bonus when not all pieces were needed to solve a puzzle (I am halfway through the game and I could solve at least 2-3 puzzles with less than the given pieces).
- If you add music, which I don't think is neccessary as I can always have music of my choosing playing in another tab, please add a mute button or better yet, start the game muted.
- In LVL 30 I experienced a bug: the Bishop was only counted on a specific field of its path although the other positions were also checkmate.
- Check the completed levels in the in the menu, so that it is immediately obvious which levels have already been completed and which ones are still open.
- You might want to have the higher levels blocked until you have cleared a number of the lesser ones, eg. player must clear 8 out of 10 in stage 1 before he can advance to the next set of ten levels in stage 2; you can also make stages for certain pieces, e.g. stage 1 is mainly rook, stage 2 is mainly queen, etc.
- For future development you could add more game modes, e.g.: a) white is at a disadvantage and has to force a stalemate b) white has a variety of pieces and has to try to checkmate with the least amount of material c) survival mode, where you begin with a full set of pieces and you lose the pieces you used in the previous LVL; every 5 LVL you can get one piece back if you solve a bonus puzzle

I think it's a very good game for anyone who has played some chess. But the number of such people may be dwindling. I might suggest making the early levels be clearly marked as tutorials (maybe with a conspicuous "TUTORIAL" showing up in the right hand info pane while you're playing those levels) until you get to level 32, with an option to skip them and go straight to the harder levels, just so people don't see many easy levels and think that the whole game is going to be easy.

It might also be nice to allow the game to run as it currently does for casual players, but also make a more difficult mode where the player has to position all of the pieces and then click a button saying "declare checkmate" when they think they've got a solution instead of having the computer automatically check it after each repositioning of the pieces. If the solution is not correct, then show a move that gets the black king out of check.

Background music and possibly sounds would also be good.

Also, I think I spotted a bug on level 60. It counted it as a solution when I had the knight at K4, bishop at QR4, and rook at Q7. But I think the black pawn should be able to advance one space to block the bishop's check.

I love chess and puzzles! Not half bad :)

It's a good concept for a game, but perhaps some better hints for novices?