Of course, how we use the Old Testament, especially, can be a little confusing. We know that certain things are directly carried forward from the Old Testament to the New. Commands regarding basic morality are a good example. "You shall not murder" and "You shall not commit adultery" are as valid in the NT as the were in the OT. In fact, the NT evens expands some of these moral principles. Jesus said, "Whoever looks at a woman to lust for her has already committed adultery with her in his heart." (Matt. 5:28)
Then there are commands given to the Jewish nation that do not apply to the church. These are not moral laws but religious regulations. The Jews could not eat pork, for example, because it was considered 'unclean'. The NT abrogates such rules. All foods are allowed under the New Covenant.
These things are clearly laid out for us, but some things are less clear. Often a principle found in the OT applies quite differently in the NT. Here is an example from Romans 10:5-9:
Moses writes about the righteousness which is of the law, “The man who does those things shall live by them.” But the righteousness of faith speaks in this way, “Do not say in your heart, ‘Who will ascend into heaven?’” (that is, to bring Christ down from above) or, “‘Who will descend into the abyss?’” (that is, to bring Christ up from the dead). But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved.
Now this might seem like a simple quotation from the OT, but it is not. In fact, the quote from the OT has been altered to fit the point that Paul wants to make and has a meaning opposite from the OT context. Paul even changes words when it suits him. Here is the OT passage that Paul quoted. (Deuteronomy 30:11-14)
For this commandment which I command you today is not too mysterious for you, nor is it far off. It is not in heaven, that you should say, ‘Who will ascend into heaven for us and bring it to us, that we may hear it and do it?’ Nor is it beyond the sea, that you should say, ‘Who will go over the sea for us and bring it to us, that we may hear it and do it?’ But the word is very near you, in your mouth and in your heart, that you may do it.
The words of God that Moses is talking are His commands. The words of God that Paul is talking about is the gospel (the word of faith). Moses talks about bringing the Law from Heaven; Paul applies this to Christ, not the Law. Moses speaks of going across the sea; Paul turns this into going into the 'abyss'. Perhaps bigger than anything, Moses is telling the Israelites to keep the Law of God in the mouths and hearts so that they can do the commands so that God can bless them. Paul tells the church that we are saved by believing in our hearts that God raised Jesus from the dead and by confessing with our mouths the Lord Jesus.
This is really quite amazing. Paul seems to turn what Moses said on its head! But we have to look at two things here. One is the fact that the principle is the same, but that the application is quite different and it even contradicts, sometimes, its OT meaning. The principle is one about revelation. God revealed the Law to Moses and therefore the Israelites had to keep it and they could do that if they kept it in their mouths and hearts. Paul, however, applies it to the gospel. We now have the gospel of Jesus Christ revealed to us so that we have no excuse not to believe and be saved.
The second important thing to understand is that we must be careful when applying certain OT principles in the NT era. Sometimes that principle has been transformed by Christ and the gospel.
With all this in mind, let's see how we can apply what Paul has said to other OT passages. We can take two passages from the OT that say something very similar to what Moses said in Deuteronomy 30.
This Book of the Law shall not depart from your mouth, but you shall meditate in it day and night, that you may observe to do according to all that is written in it. For then you will make your way prosperous, and then you will have good success. (Joshua 1:8)
Blessed is the man who walks not in the counsel of the ungodly, nor stands in the path of sinners, nor sits in the seat of the scornful;But his delight is in the Law of the Lord, and in His Law he meditates day and night. He shall be like a tree planted by the rivers of water, that brings forth its fruit in its season, whose leaf also shall not wither; and whatever he does shall prosper. (Psalm 1:1-3)
Both of these OT quotations talk about the same thing, meditating on the Law of Moses. Should Christians do this? We have to say that in a way we should do it, but we have to transfer this principle into NT terms. We do need to meditate on the words of God, but not just on the Law of Moses. We need to meditate in the New Testament much more than in the Old. That is a proper application of the OT and I think that most Christians would apply it this way. However, what Paul does in Romans 10 is our justification for "translating" OT principles and making them applicable to the gospel.
We do need the Old Testament as well as the New. What we also must realize is that we cannot just yank anything out of the OT and apply it the NT era. We can easily get into foolishness and error that way.