Does the Church ever dispense from these diriment impediments?
She never dispenses and indeed she cannot dispense from those diriment impediments that arise from strict natural law or the divine law, as are, for instance, impotency, or the consummated marriage, or consanguinity in the direct line, or in the collateral line between two very nearly related as brother and sister. But as regards the other impediments which in the main are due to her own ruling she can dispense from them, but only does so for very grave reasons.
Is there not a diriment impediment that does not refer to the condition of the contracting parties, but is extrinsic to them?
Yes; and it is the impediment of clandestinity.
What is clandestinity?
It is a law of the Church which declares null and void the marriage contracted between baptized Catholics, or those who sometime or other were Catholics -- and between baptized and non-Catholics whether the latter be baptized or not -- and between Latins and Orientals-if the marriage is not contracted before the parish priest or before the bishop of the place, or before a priest delegated for this purpose, with at least the presence of two witnesses. If the parish priest or the bishop absolutely cannot be present or only under the greatest difficulties, and there is danger of death to one of the parties, or the difficulties be of such nature that it is impossible for either the parish priest or the bishop to be present for the space of a month, the marriage can be contracted validly with the testimony of two witnesses only (Code, Canons 1094-1099).
Next - The Catechism of the Summa - Tertia Pars - XLIII. OF THE SACRAMENT OF MATRIMONY; OF ITS NATURE, IMPEDIMENTS, DUTIES; OF DIVORCE; OF SUBSEQUENT MARRIAGE; AND OF ESPOUSALS (F)