Annulment

Technically, the church of Rome regards marriage as indissoluble. Hence, its opposition to divorce. There is, however, a very large loophole, and that's annulment. This involves the theory that some unions lack one or more necessary conditions to be "valid" marriages in the first place. When the church of Rome nullifies one of these unions, it is merely giving formal recognition to the preexisting fact that this was never a valid marriage. See here:

http://www.vatican.va/archive/ENG1104/__P3V.HTM

Can.  1083 §1. A man before he has completed his sixteenth year of age and a woman before she has completed her fourteenth year of age cannot enter into a valid marriage.

The age threshold for males is somewhat arbitrary. That would invalidate many Jewish marriages. From what I've read, puberty is the Jewish threshold. 

Can.  1085 §1. A person bound by the bond of a prior marriage, even if it was not consummated, invalidly attempts marriage.

This assumes that a wedding ceremony alone, absent consummation, is sufficient for a valid marriage. 

Can.  1091 §1. In the direct line of consanguinity marriage is invalid between all ancestors and descendants, both legitimate and natural.
§2. In the collateral line marriage is invalid up to and including the fourth degree.
§3. The impediment of consanguinity is not multiplied.
§4. A marriage is never permitted if doubt exists whether the partners are related by consanguinity in any degree of the direct line or in the second degree of the collateral line.
Can.  1092 Affinity in the direct line in any degree invalidates a marriage.
Can.  1093 The impediment of public propriety arises from an invalid marriage after the establishment of common life or from notorious or public concubinage. It nullifies marriage in the first degree of the direct line between the man and the blood relatives of the woman, and vice versa.
Can.  1094 Those who are related in the direct line or in the second degree of the collateral line by a legal relationship arising from adoption cannot contract marriage together validly.

Doesn't that invalidate the marriage of Sarah and Abraham? She was his stepsister. 

Perhaps Rome would try to salvage the condition by asserting that prohibited degrees of affinity are variable in time or place. But isn't canon law respecting marriage supposed to be grounded in natural law rather than social conventions?

Can.  1103 A marriage is invalid if entered into because of force or grave fear from without, even if unintentionally inflicted, so that a person is compelled to choose marriage in order to be free from it.

Doesn't that invalidate Hosea's marriage to Gomer? Left to his druthers, he would not knowingly marry a promiscuous woman. He was acting under duress. God commanded him to marry her. 

Can.  1055 §1. The matrimonial covenant, by which a man and a woman establish between themselves a partnership of the whole of life and which is ordered by its nature to the good of the spouses and the procreation and education of offspring, has been raised by Christ the Lord to the dignity of a sacrament between the baptized.
Can.  1096 §1. For matrimonial consent to exist, the contracting parties must be at least not ignorant that marriage is a permanent partnership between a man and a woman ordered to the procreation of offspring by means of some sexual cooperation.
Can.  1102 §1. A marriage subject to a condition about the future cannot be contracted validly.

Doesn't that invalidate the marriage of Mary and Joseph?

i) After Gabriel intervened to inform Joseph of God's will, it's not as if Joseph was at liberty to carry through with his intentions (pace Can. 1103). He'd incur God's displeasure.

ii) Both Mary and Joseph were betrothed with the expectation that they'd have a normal marriage rather than a platonic marriage. A prior understanding of what their marriage would amount to. But according to Catholic dogma, Mary was a perpetual virgin. If so, they became betrothed under false pretenses. Their matrimonial consent was subject to a future condition, which was thwarted by Mary's perpetual virginity.

It's like signing a contract, only to have the terms of the contract altered after the fact. That's not what you agreed to.

iii) If marriage is ordered to the procreation of offspring by means of some sexual cooperation, and that's a necessary condition of matrimonial consent, then that invalidates their marriage–given Mary's perpetual virginity.

So on no fewer than three separate grounds, Mary and Joseph were never validly married–by Catholic criteria. 

Perhaps Rome would try to salvage the condition by asserting that Mary and Joseph are a special case. But, once again, isn't canon law respecting marriage supposed to be grounded in natural law? If so, aren't these conditions a matter of principle? Something absolute, given human nature?