OK, one
good point, and one
bad point need to be made here.
The problem needs to be rephrased as such: A barber shaves all those men that do not shave themselves, and only those men who do not shave themselves. Otherwise, there is nothing wrong with him shaving himself. This also affects the self-repairing robot.
(because it is
missing the point)
There is nothing wrong with this problem if the barber is female.