This is a big question that’s very difficult answer completely without offending somebody or sounding like I am avoiding the question.
There are some technical considerations to keep in mind. First, we must remember that the Bible was written by many authors over a span of thousands of years, thousands of years ago, in two languages that are no longer spoken by anybody on Earth and on materials that were very rare and often quite fragile. If the Bible were any other book, it would be roundly celebrated as the best preserved, most consistent, and universally relevant book in the history of the world. If it were any other book, an inconsequential mismatch of detail would be quickly cataloged as a typo and never mentioned again. In truth, judged by the standards of far more recent manuscripts, the Bible stands up as extraordinary, unique, and unexplainably superior to any competitor.
Second, we need to keep in mind the changing face of history and the “errors” it may indicate. For example, for many years Bible critics emphatically stated that no archeological evidence existed to support the contention that criminals were crucified during Jesus’ time. However, a pair of heel bones were recently found. These bones had been nailed together and were dated to be contemporary to Jesus’ Jerusalem. With that discovery, the Bible was suddenly vindicated, the “error” vanished, and critics moved on to their next “air-tight” case.
Lastly, remember that an error is often in the eyes of the beholder. Luke says that Jesus was born in a stable while Matthew says that the wise men visited Mary in a house. Critics say that this is a contradiction between the two accounts but a more balanced reading shows that there is no reason to infer that the events happened simultaneously. It’s completely possible that the wise men came some time after Jesus’ birth – allowing a period of several days, weeks or even a year for Joseph and Mary to settle down in a house.
Realistically, the question of the Bible’s inerrancy has often divided the church from the world and occasionally has divided the church within itself. But the real question is not whether 100 generations of monks and scribes were able to copy every letter perfectly by hand. More important is the Bible’s unparalleled history of saving lives, changing the world and speaking wisdom and truth into the most difficult situations. Next to that profound truth, a person’s inability to find where Cain’s wife came from seems less and less important.
“All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, thoroughly furnished unto all good works” (2 Timothy 3:16-17).