If God unequivocally states in Malachi that He hates divorce, why then does Jesus state that it permissible on the grounds of adultery in Matthew. Is this some sort of compromise on God's part?
Yours appears to be a very valid question. There are other passages that may apply as well, however.
First, there are those that would argue that "putting away" in Malachi 2:16 is not talking about divorce, although some newer versions use "divorce" rather than translating the Hebrew word, which simply means to send away. It is used more often for things other than divorce, such as when God sent Adam from the garden (Genesis 3:23), when Noah sent a raven from the ark (Genesis 8:7), when Rebekah's brothers sent her to Isaac (Genesis 24:59), or when someone stretches forth his hand (Genesis 3:22). I do believe, however, that the context would seem to indicate divorce in Malachi 2:16. So my further remarks will assume that he means divorce.
Do the statements of Jesus that allow for a possible exception to the "no divorce" rule amount to a compromise on God's part? If so, it certainly wouldn't be the first time. Jesus even says that God allowed divorce under the Law of Moses as a compromise. "And Jesus answered and said unto them, For the hardness of your heart he wrote you this precept." (Mark 10:5) On the other hand, Jesus is also saying that the rule about divorce for fornications (the Greek language uses the plural) was from the beginning.
We find another case, under the Old Testament, in which divorce was sanctioned, perhaps even demanded, by God. Chapter 10 of Ezra recounts a circumstance in which the people of Israel after the Babylonian captivity swore to God that they would divorce their foreign wives. Not only was this approved by the people, but also by God.
Getting back to the reason Jesus gave for divorce, we may also see valid reasons for this exception. These are based on two possible interpretations of the scripture, both based on contract law.
Some people would say that he is talking about putting away wives who were "damaged goods" before the marriage, because he says fornication and not adultery. The thought here is that a marriage that took place under false pretenses (that the wife claimed to be a virgin when she wasn't) is not a valid contract. Under almost every legal system fraud may be used to void a contract. Thus Jesus may be saying that when a man finds out that his wife lied to him about her virginity he may choose to divorce her. In this case, however, if he fails to divorce her as soon as he finds out then he forfeits the right to do so later.
Another interpretation may be based on the unusual way Jesus phrased the exception. He did not say "fornication" as most versions translate it, but "fornications" in the plural. This might carry the idea that one instance of infidelity is not grounds for divorce, but more than one could be. (I am not saying that this is necessarily the right interpretation, because some might take that as license to commit adultery once, which I don't think is a valid conclusion.) The basis behind this thought is that if one party to the marriage continually violates the contract then the contract may be declared void or breached.
The bottom line in the issue of marriage and divorce is that God expects us to fulfill our vows. God does not like fraud, and he does not like lying. When one party has violated the marriage contract, the contract is voidable by the other party. Essentially, a divorce may sever the marriage because one party has already severed it. In Malachi the putting away that God specifically opposed was "dealing treacherously" with the wife. This would also carry the idea of fraud or breach of covenant. God wants us to stay married and, if possible, live together in a marriage. But God has allowed for the party who has kept a covenant with his wife to end a marriage that the wife has already destroyed.
Finally, it is important to point out that allowing a divorce is not the same as commanding it. It may have been commanded in Ezra 10, but other than that circumstance we are allowed to continue in a marriage in spite of fornications on the part of the other spouse.