In large transformers,core and core clamping metal structures are individually insulated and isolated from ground and then shorted together to tank which, in turn, is earthed to ground.When core or coreclamp gets another inside earthing to metal tank,due to damage in the insulation structures( usually press board or FRP) there is a chance of circulating current through the double earthed part.The problem is more in case of core clamp due to voltage difference developed from leakage flux at full load.This current can some times cause arcing in current path and even melting of metal.This can be detected from DGA ( dissolved gas analysis of oil)results.Many times, such problem may not be there,say when second earthing is at bottom of core to tank.( a location where there will be no leakage flux )To prevent circulating currents, one way is to add a resistor in series to the double earthed component path so that circulating current is reduced.Some times the designed earth at tank top is separated out as the failed path inside will act as earthing.
My experience is that inadvertent earth in core laminations is not a issue and nothing need to be done.