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Well, concerning the eternal validity of the Old Testament, we Catholics teach and believe that:

121 The Old Testament is an indispensable part of Sacred Scripture. Its books are divinely inspired and retain a permanent value,92 for the Old Covenant has never been revoked.
122 Indeed, "the economy of the Old Testament was deliberately SO oriented that it should prepare for and declare in prophecy the coming of Christ, redeemer of all men."93 "Even though they contain matters imperfect and provisional,94 The books of the Old Testament bear witness to the whole divine pedagogy of God's saving love: these writings "are a storehouse of sublime teaching on God and of sound wisdom on human life, as well as a wonderful treasury of prayers; in them, too, the mystery of our salvation is present in a hidden way."95
123 Christians venerate the Old Testament as true Word of God. the Church has always vigorously opposed the idea of rejecting the Old Testament under the pretext that the New has rendered it void (Marcionism).

Regarding the validity of the Jewish law, we teach and believe that:

1961 God, our Creator and Redeemer, chose Israel for himself to be his people and revealed his Law to them, thus preparing for the coming of Christ. the Law of Moses expresses many truths naturally accessible to reason. These are stated and authenticated within the covenant of salvation.
1962 The Old Law is the first stage of revealed Law. Its moral prescriptions are summed up in the Ten Commandments. the precepts of the Decalogue lay the foundations for the vocation of man fashioned in the image of God; they prohibit what is contrary to the love of God and neighbor and prescribe what is essential to it. the Decalogue is a light offered to the conscience of every man to make God's call and ways known to him and to protect him against evil:
God wrote on the tables of the Law what men did not read in their hearts.13
1963 According to Christian tradition, the Law is holy, spiritual, and good,14 yet still imperfect. Like a tutor15 it shows what must be done, but does not of itself give the strength, the grace of the Spirit, to fulfill it. Because of sin, which it cannot remove, it remains a law of bondage.
According to St. Paul, its special function is to denounce and disclose sin, which constitutes a "law of concupiscence" in the human heart.16 However, the Law remains the first stage on the way to the kingdom. It prepares and disposes the chosen people and each Christian for conversion and faith in the Savior God. It provides a teaching which endures for ever, like the Word of God.
1964 The Old Law is a preparation for the Gospel. "The Law is a pedagogy and a prophecy of things to come."17 It prophesies and presages the work of liberation from sin which will be fulfilled in Christ: it provides the New Testament with images, "types," and symbols for expressing the life according to the Spirit. Finally, the Law is completed by the teaching of the sapiential books and the prophets which set its course toward the New Covenant and the Kingdom of heaven.
There were . . . under the regimen of the Old Covenant, people who possessed the charity and grace of the Holy Spirit and longed above all for the spiritual and eternal promises by which they were associated with the New Law. Conversely, there exist carnal men under the New Covenant still distanced from the perfection of the New Law: the fear of punishment and certain temporal promises have been necessary, even under the New Covenant, to incite them to virtuous works. In any case, even though the Old Law prescribed charity, it did not give the Holy Spirit, through whom "God's charity has been poured into our hearts."18

I think that the core of the debate related to the identity of Israel within the People of God. Are there two People of God, Israel and the Church? Or only one? If one - and this is what we believe - can Jews exist as Jews in the People of God, or not?

Throughout history, the answer - from both sides - has been a resounding "no." But after the Holocaust, we on the Christian side are wondering if we blundered by insisting that supersessionism meant the suppression and absorption of Jewish identity into Gentile Christianity. Of course, the Holocaust has led most Jews to insist more than ever on their separate uniqueness and election.

That's where the debate stands and I don't mean to solve it here, except to insist upon the Christian vocation of Love.

~Theo