Dab a cotton ball into a small amount of calamine lotion. Gently pat the cotton ball all over the pointe shoes, paying special attention to dirty areas. The calamine lotion will absorb some of the larger stains and give your pointe shoes a clean, even tone.
Rubbing alcohol is preferable to water because is dries more quickly. lightly soak a cotton ball in rubbing alcohol and dab across the box of the shoe at the place where it should bend on demi-pointe. Never pour the alcohol or water directly onto the shoe as that could weaken too much of the shoe and make it unwearable. After softening the boxes in this manner, it is especially important to allow them to dry out completely before wearing.
All you need to do is carefully coat the frayed edges with clear nail polish. The nail polish will harden and seal the threads to prevent further fraying, and you won't be able to see it because it is clear.