It may seem so, but the example given in Scripture is that of Sodom, which was destroyed for their prevelant and blatant sexual conduct (most notably homosexuallity). The law of Moses says that their shall be no Sodomites among the people of Israel. This shows that the act was a sin in the eyes of God before moses, and is used by Jude in the New Testiment to show that it is still a sin.

Paul, from what I have read does not use the Leviticus to teach this doctrine as he was preaching to people who did not have, nor believed, in the writtings of Moses. (He may have in his epistle to teh Hebrews.)

As for some parts of teh law applying only to the time of Moses, and otehrs applying to all times, this is very generally understood in the New Testiment, and many times the apostles speak out against followingthe Law of Moses. However, those laws that are still in effect were taught by them as being the laws of God. So, it would be safe to say, if they did not teach the law in the New Testiment it did not apply. (Now, I do not exactly agree with this, but for one who only believes in the Bible it is the only really logical way to look at it.)