The carpet and wood floors will be a problem. Water cannot be left to sit on wood floors, it will destroy the finish. You most likely have wood subfloor (plywood) under the carpet, too. That combined with the carpet and padding could mold if it gets and stays wet.
In those rooms you could also try placing the water bowls in very large underbed storage bins. They have lower sides which could be stepped over - this way your kitten could play in the water as much as he wants.
Don't worry, he'll find other ways to make you crazy when he's older! I have four adult cats, and while less trouble than kittens, they're still a handful... to make it worse I took in three feral kittens.
