Rumors abound...

a) Joker is only "scarred" and simply puts on the grease paint.
b) His skin continues to flake off and uses the grease paint as a desperation attempt to keep some semblance of a normal face.
c) It's a reverse... the paint look is his actual face and the "normal skin" is his disguise, a la Nicholson in the first Bats.
d) He's a robot.

He fixes the cable?