Looks pretty good and works well now, but the controls are bit wonky. I tend to drop off the edges of stuff because it's hard to keep yourself oriented in a steady position, and you automatically drop when the ledge you're hanging on becomes blocked by a solid wall. Maybe you could do something about that.
Also, the climbing speed in general is a bit slow. Climbing up single blocks takes longer than just jumping up, and climbing two at a time takes longer than just mining away the block on top would. With some improvements to the movement speed this would be a fairly nice alternative to Le Parkour, though.