Case in point: King David's reign. We're told that David rules forty years. And during that reign there was the strange episode of his son Absalom. To make a complicated story as simple as possible, one of David's sons (Ammon) decides to rape his own sister (Tamar). After waiting two years (2nd Samuel 13.23) for his target's guard to be down, Absalom avenges his sister by murdering his brother. Fearing the king's wrath, Absalom flees and remains in exile three years (2nd Samuel 13.38). Eventually he is recalled but still forbidden to see the king for two more years (ibid 14.28), after which he is fully pardoned. Another forty years pass (ibid 15.7), during which time Absalom becomes far more popular than David and ends by stating a coup against him to usurp the throne.
The problem, of course, is that we have a detailed account of events taking place over forty-seven years which are only part of David's forty-year reign. The reference in 2nd Kings 15.7 is obviously factually wrong.
A second, simpler, and much more amusing example of bad chronology occurs in 2nd Chronicles 21.20 vs. ibid 22.2. The first of these relates how King Jehorum reigned eight years, having become king at the age of thirty-two (32+8 = 40). The second relates how he was succeeded by his son Ahaziah, who reigns only one year after becoming king at the age of forty-two.
So: explain how a man who dies at age forty turns over the kingship to his son, who is already forty-two at the time.
Of course, this is only a problem if you think that, since the Bible is the word of God it has to be perfect. But the world, too, was created by God, and it's far from perfect. So why shdn't the same be true of the Good Book?
current reading: THE SCROLL OF DEATH by David Stuart Davies [1998 & 2009], part of THE FURTHER ADVENTURES OF SHERLOCK HOLMES series.