The coat is the biggest grooming hurdle and can fall prey to shedding, a greasy consistency and mats (clumps of matted hair that are anchored to your cat's coat). Remember to comb gently from front-to-back and reassure your cat with a soothing voice. Do this as much as needed to keep shedding and knots to a minimum. The proper combs and brushes can help.
For more information in grooming your kitty, go to Grooming Your Cat.