The "continuous charge" version of Coulomb's law is never supposed to be applied to locations for which | r − − r ′ | = 0 because that location would directly overlap with the location of a charged particle (e.g. electron or proton) which is not a valid location to analyze the electric field or potential classically. Charge is always discrete in reality, and the "continuous charge" assumption is just an approximation that is not supposed to allow | r − − r ′ | = 0 to be analyzed.