What is the ruling on employing a mentally disabled son in a company - on paper only - to receive a monthly salary without him actually performing work, and is this salary considered permissible?

If the manager employs your son on paper with the permission of the factory owners, then there is no harm in the salary; it is a gift and a grant, and it may be for social responsibility. However, if the factory owners do not permit this, then it is not permissible, and the money must be returned or spent on the factory's interests.