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.