If you have the items you are trying to drop equipped on your item slots the game won't allow you to drop them. So unequip the item and then drop it, as for sliding just hold B when on a ladder and your character will slide down.
The Bird of the Hermes is my name, eating my wings to make me tame.
As others said hold b on a ladder to slide. However as with quite a lot of the controls it's fairly tempermental. Basically you can't be moving at all and also seems that if you press B before your character has finished the animation of getting on the ladder then it won't work.