For some time I've felt dissatisfied with the tripartheid division of the law in which the ethical demands remain in full validity while the ceremonial and civil ones fall away under the New Covenant--as explained, for example, in Van Gemeren's contribution in this volume. It seems quite artificial to me. Yet there has also seemed to me to be something about the more moral injunctions of the Mosaic code which can be claimed to appeal to something beyond the Mosaic code itself--as if God's (preceptive) will, eternal, unchanging, fixed, utterly real and objective in itself, came down to earth 3500 years ago to a people called Israel, and while some of the laws laid out for this people were extremely tied to that particular culture and locale, others were much closer to that eternal divine will--and therefore can in no way be "abolished," despite all the radical changes that come with the dawning of the new day wrought by Jesus' death and resurrection. In fact, they are confirmed.
And so I think Stephen Westerholm expresses my mind best on the subject, from what I have found so far. Toward the end of his most central piece on Paul, Perspectives on Paul Old and New, he writes:
The traditional interpretation that sees believers free from the "ceremonial" but not the "moral" demands of the law is not quite Pauline, but at the same time it is not without a point. Paul himself never makes such a distinction; his declarations of freedom from the law include all its demands without further specification; they mean, not simply that believers are delivered from the obligation to observe particular (ceremonial) statutes, but that they serve God in a new way, not "by the letter" but "by the Spirit." On the other hand, the distinction between ceremonial and moral is not without a point, since Paul does think the (moral, patently not the ceremonial) commands of the Mosaic law embody the expectations of goodness inherent in the human condition. And Christians, too, are to do the "good." Their doing so, however, should be very different from a formal compliance with requirements externally imposed; rather, it should represent an expression of their submission and devotion to God and of the fruit his Spirit bears in their lives. (p. 437)
Richard Gaffin provides an equally helpful statement on the topic in his wonderful little By Faith, Not by Sight:
It is undoubtedly true that almost always when Paul refers to "law" or "the law," he has in view the body of legislation given by God through Moses to Israel at Sinai, that legislation marking out the period of covenant history until Christ. He is also clear that, as a specific codification belonging to that era, the law has been terminated in its entirety by Christ in his coming (e.g. Rom. 6:14; 7:6; 10:4; 2 Cor. 3:6-11; Gal. 3:17-25). At the same time, however, it seems difficult to deny that in a statement like Romans 7:12 . . . or in Romans 13:9, where several of the ten commandments function as exhortation incumbent on the church . . . Paul recognizes that at its moral core, the "Torah in the Torah" as it could be put, the Mosaic law specifies imperatives that transcend the Mosaic economy. Included within that law are imperatives that are bound up with the indicative of the creator-creature relationship from the beginning and, so, are enduring because of who God is. In its central commands the law given at Sinai, notably the Decalogue, reveals God's will, inherent in his person and so incumbent on his image-bearing creature as such, regardless of time and place, on non-Jew as well as Jew. (31-32)