Let me summarize what we've discovered so far: Even though God declared His hatred of divorce, He gave no indication before or during the old covenant that remarriage was a sin, with these two exceptions: (1) the twice-divorced or once-divorced once-widowed woman remarrying her first husband and (2) the case of a divorced woman marrying a priest. Furthermore, God gave no indication that marrying a divorced person was a sin for anyone except priests.
This stands in apparent contrast to what Jesus stated about divorced people who remarry and those who marry divorced persons. Jesus said such people commit adultery (see Matt. 5:32). So we are either misunderstanding Jesus or Moses, or God changed His law. My suspicion is that we might be misinterpreting what Jesus taught, because it would seem strange that God would suddenly declare something to be morally sinful that was morally acceptable for fifteen hundred years under a Law that He gave to Israel.
Before we tackle this apparent contradiction more fully, may I also point out that God's permission of remarriage under the old covenant did not carry any stipulations that were based on the reasons for one's divorce or the degree of guilt one incurred in the divorce. God never said that certain divorced people were disqualified from being remarried because their divorce was not for legitimate reasons. He never said that some people were uniquely worthy to remarry because of the legitimacy of their divorce. Yet such judgments are often attempted by modern ministers based on one-sided testimony. For example, a divorced woman tries to convince her pastor that she is worthy to be permitted to be remarried because she was just the victim of her divorce. Her former husband divorced her--she didn't divorce him. But if that pastor was given an opportunity to hear her former husband's side of the story, he might become somewhat sympathetic for him. Perhaps she was a beast and shares some blame.
I've known a husband and wife who both tried to provoke the other to file for divorce so that they could avoid the guilt of being the person who filed for the divorce. They both wanted to be able to say after the divorce that it was their spouse, not them, who filed for divorce, thus making their subsequent second marriages lawful. We may be able to fool people, but we can't fool God. For example, what is His appraisal of the woman who, in disobedience to God's Word, continually withholds sex from her husband and then divorces him because he became unfaithful to her? Is she not at least partly responsible for the divorce?
The case of the twice-divorced woman we just read about from Deuteronomy 24 does not say anything about the legitimacy of her two divorces. Her first husband found some "indecency" in her. If that "indecency" had been adultery, she would have been worthy of death according to the Law of Moses, which prescribed that adulterers be stoned (see Lev. 20:10). So, if adultery is the only legitimate reason for divorce, perhaps her first husband did not have good reason to divorce her. On the other hand, perhaps she had committed adultery, and he, being a righteous man like Mary's Joseph, "desired to put her away secretly" (Matt. 1:19). There are many possible scenarios.
Her second husband is said to have simply "turned against her." Once again, we don't know who was to blame or if they shared the blame. But it doesn't make any difference. God's grace was extended to her to remarry anyone who would take the chance on a twice-divorced woman, with the exception of her first husband.
"But if people are told that it is lawful for them to remarry after divorcing for any reason, that will encourage them to divorce for illegitimate reasons," it is often claimed. I suppose that might be true in some cases of religious people who are not truly attempting to please God. But trying to restrain people from sinning who are not submitted to God is a fairly useless exercise. People who are truly submitted to God in their hearts, however, are not trying to find ways to sin. They are trying to please God. And those kinds of people usually have strong marriages. Moreover, apparently God was not too concerned about people under the old covenant divorcing for illegitimate reasons due to a liberal law of remarriage, because He gave Israel a liberal law of remarriage.
Should we avoid telling people that God is willing to forgive them of any sin, lest they be encouraged to sin because they know that forgiveness is available? If so, we'll have to stop preaching the gospel. Again, it all comes down to the condition of people's hearts. Those who love God want to obey Him. I know very well that God's forgiveness would be available for me if I ask for it, no matter what sin I might commit. But that doesn't motivate me at all to sin, because I love God and have been born again. I've been transformed by God's grace. I want to please Him.
God knows there is no need to add one more negative consequence to the many unavoidable negative consequences of divorce in hopes of motivating people to remain married. Telling people with troubled marriages that they better not divorce because they will not be permitted to ever remarry provides very little motivation for staying married. Even if he believes you, the prospect of a life of singleness compared to a life of continual marital misery sounds like heaven to the miserably-married person.
See Divorce and Remarriage - Part 5