Apple cider vinegar may help remove moles, but it doesn't always work for everyone. I'd say try it. You just soak a cotton ball in the vinegar and bandage over mole. You would do this at night while sleeping. Just be sure the mole is not melanoma.
It can and does help with warts. There are also herbs you can use to get rid of warts.
Soak a piece of cotton ball with the vinegar. Rub it on gently, and then bandage it overnight. Clean it off in the morning, and then put a bandage on it. You'll have to repeat this until the wart is gone.
You can also use the juice of a dandelion stem. Rub the wart gently with an emery board. Apply the dandelion juice, and bandage it. You will have to repeat this for several times.
You can also use banana, potato, garlic and believe it not duct tape.
While some may poo poo folk remedies, they CAN and do work for a number of illnesses. They are not always just old wives tales.
PS. Apple cider vinegar can be used for many home remedies. Never sell short "folk remedies".