They could easily stop all but the most determined cheaters by cutting out the link to the game. Currently you just have to click on the game link to get the solution!
I would like to see my rating progress, success rate, tries on daily, weekly and monthly base, highest and lowest rating. Where i am compared to other users is useful too, but has not that high priority for me.
I haven't read the rest of the thread, but I have to say that rankings for puzzle rankings would not be a good idea. I say so because it is allowed to use a computer (Rybka, Stockfish, etc.). It would just be artificial rankings.