You are going to have to clean the spa cover every so often. I use a bleach and dish detergent mixture on the outside and scrub it with a deck brush, then use 303. I just tried a power washer on it and it came out squeaky clean, once it dries I'll put the 303 on it.
For the inside you need to use either the chlorinated water that you shock with and a rag, bleach and water with a rag or a bleach impregnated wipe to clean and kill the mold/bacteria that may be growing. Some people have put 303 on the inside as well.
The inside will get growths on it and may start to smell after a while.