The dead space between the inside of the door and the beginning of the shelves is valuable space when outfitting a linen closet. Door racks are intentionally made narrow to fit into these spaces, so they're perfect for storing toiletries and cleaning products, thus freeing up precious shelf space. Just make sure the shelves are tall enough to contain their contents so you're not constantly picking up fallen bottles every time you open the door.
If you have a different area where you store your toiletries, then consider mounting towel racks or hooks on the inside of the door. If your closet is located in your bathroom, this can serve as a great space saver for towels that need to dry out before you use them again. If you use your linen closet more for dining linens, like tablecloths and cloth napkins, the door is an excellent place to hang long linen tablecloths that need special care to keep from getting wrinkled.