Ya, what kitytize said!
A heavy bowl or non-skid pads underneath it will stop the dragging. Unfortunatly I don't think there's anything to do about the playing that won't completly deter the cat from the water as a whole. Wickett plays in his water too. In fact, that's how he drinks it... he'll dunk his paw in and lick the water off... then shake!
my walls have lots of water spots. It's especially fun when he does it right after a good dig in the litter box... then theres litter in the water and it usually clumps to his toe tufts.