Check every wall carefully before you move in. First and foremost, the paint should not be chipped and it should be consistent throughout the apartment. Make sure there are no stains on the walls. Also, make sure the paint isn't comprised of poisonous materials. If your walls are wood-paneled, be sure that there aren't any loose or rotten boards.
Look for holes where posters or pictures once decorated the walls. When you're moving out, you'll have to fill in the holes that you've added. You can use caulk or spackle to fill in the holes. Check the baseboards to see if they are damaged as well.