Does the Old Testament contain instructions that don't apply to Christians today?
Yes. The Old Testament includes instructions given to Israel under the Law that do not apply to believers today. Leviticus 5's rule about touching dead animals and bringing a trespass offering is one example; Scripture says such regulations are not for us now, and the Apostle Paul is the Gentile Apostle.
Les teaches from Leviticus 5 that if a person touched any unclean thing—such as the carcass of an unclean beast, cattle, or creeping thing—even if it was hidden from him, he became unclean and guilty. The prescribed remedy was to bring a trespass offering to the Lord for his sin. Les points out that nobody with a brain would do this today because this regulation was not for us; it was Israel under the Law. He illustrates that if he had to return to the Temple in Jerusalem every time he touched a dead animal, he would spend most of his time on overseas flights. We are not under that kind of Law. Over and over the Old Testament gives instructions that do not apply to us, and it would be ridiculous to try to keep all of it. The Bible did say these things, but it said them to Israel under the Law. So it is appropriate to recognize that the Apostle Paul is the Gentile Apostle.