To provide some background for discussion of the law of God, it is important to understand the categories involved:
The law of God in the Old Testament is of three kinds:
Moral law, because it reflects the character of God, is enduring and immutable. It never was and it never will be permissible to worship any god but God, it never was and never will be permissible to worship God other ways than He ordains, it never was and never will be permissible to dishonor God's name, it never was and never will be permissible to appropriate all seven days of the week for our work, it never was and never will be permissible to dishonor the authorities over us, to kill, to steal, to lie, to covet, and so forth. In short, it is always the case (for all history) that we must love the Lord our God wholeheartedly and love our neighbor as we love ourselves.
Under the Adamaic, Noahic, Abramic, Mosaic, and Solomonic administrations of the covenant of grace, the worship of God was manifested in certain outward ceremonies that were designed to point to Christ. Eminent among these ceremonies were the rite of animal sacrifice, the practice of tabernacle and later temple worship, and in some cases a specialized priesthood. These things all have been fulfilled in Christ, the one true and perfect sacrifice. He is our high priest and his sacrificial work is finished. Consequently there is no more sacrifice and no more priestly class among us. There were other associated ceremonies as well, such as dietary laws and laws related to physical cleanliness as a picture of spiritual cleanliness. All these ceremonial laws, being fulfilled in Christ, have been done away.
3. Civil / Judicial / Juridical
This third category of laws were the laws specific to the Mosaic administration of the nation of Israel. They are the laws by which the country was run. They are not binding on all humanity. Nevertheless, they are important as to their "general equity," by which I mean that they show to us a just system of government. There are moral aspects of the civil law of Israel, and these moral aspects remain significant. There were circumstantial aspects, and these aspects necessarily vary under different circumstances. Finally, there were ceremonial aspects, and these aspects have been fulfilled or supplanted in the New Testament.
There are four major (and numerous minor) errors that arise from holding to expired portions of the law (Judaizers and "Extreme" Theonomists) or to disposing of still-relevant portions of the law ("Extreme" Two-Kingdomists and "Extreme" Dispensationalists / Antinomians).
Judaizers seek to impose part (or perhaps all) of the ceremonial law on Christians. Thus, for example, the Judaizers argue that it is necessary for Christians to be circumcised.
2. "Extreme" Theonomists
The term "theonomist" has a wide range of meanings. In some cases, folks who call themselves "theonomists" will insist that virtually all and every detail of the Mosaic law with respect to the Nation of Israel must be followed. The problem with this approach is that it overlooks the fact that the Mosaic law was tailored to two particular forms of government and accompanied a nation-state that has ceased to be.
3. "Extreme" Two-Kingdomists
I am using the term "extreme" here because I'm not sure all "two-kingdom" folks would say this description applies to them. In some cases, it appears that "two-kingdoms" folk treat the civil law of Israel as though it were entirely ceremonial. Thus, these folks say that the civil law is essentially done-away-with and consequently for instruction on how governments should be just, we must appeal exclusively to "natural law," the light provided by God in general revelation.
4. "Extreme" Dispensationalists / Anti-Nominians
"Extreme" Dispensationalists and also Anti-Nominians take the view that all the laws of the Old Testament are done away with, including the moral law. This error arises from a failure to understand the nature of the moral law, and the relation of God to the law of God. God does not change, and consequently the definition of morality does not change.
The issue of God's law is not a simple one to be handled carelessly or callously. We must be careful to observe to do all that God has commanded us, and yet we need to be careful not to bind men's consciences beyond what the Word of God states. Excess in the first regard leads to legalism, excess in the second regard leads to antinomianism. There is one way to see the path to stay on it, without going either to the left or to the right: that one way is by careful attention to the Word of God in the Holy Scriptures.