I have two tanks in my living room and both are on carpet. There's no stability issues from the carpet and I don't have any real water issues unless I'm doing a whole lot of work. Even then, I just through a towel down to catch any splash or spillage. I havn't noticed any marks or stains on the rug near my tanks.
Now I said there were no stability issues from the carpet, but I have a very minor stability issue from the floor itself. (which i'm surprised no one here has mentioned yet) Fish tanks add a LOT of weight to your floor. Be sure where you are going to have it will support the total weight of not just the tank and stand but all the water, rocks and equipment you're going to pile onto that thing. (FWIW
, water weighs 8.3 pounds per U.S. gallon)