In deference to the inerrantists (and I hope that DDG posts here with a needed clarification on what “inerrancy” meant to the early fundamentalists, as opposed to the entrenched literalists of today), it’s important to note that their view is that the Bible is inerrant in the original autographs and when read properly.
The former is quite clear: a given translation, or the extant Hebrew and Greek texts, may not be clear and may lead one into error through misapprehension of what it really means, but the original text did not have these problems. Hence any supposed internal contradiction would be rendered moot if we just had what Moses or Isaiah or Luke or Paul originally wrote.
Regarding the latter, no inerrantist suggests that the Bible does not contain examples of various literary genres, and that some of these are not to be taken as literal statements. For example, Revelation is written in apocalyptic style, where the meaning is concealed from the casual reader but clear to the faithful. Hence one need not believe that there will appear a seven-headed, ten-horned flying purple people eater to qualify as the Beast; this is considered as symbolic of something (the original or a resurgent Roman Empire is the commonly suggested referent) and not a literal description of something predicted.
With regard to His4Ever’s stance, however, it’s been my own stance that the intent of God comes through in the texts despite the frailties of the human writers, who can and did err in a variety of ways. There are, in fact, numerous instances of preserved controversies where both sides are represented. To avoid going into great depths, consider the fact that the Book of Ruth, giving the account of a young widow, her faith journey and remarriage, can be shown by internal linguistic evidence to have been written in its present form at about the time of the Return from Exile. Now, the extant account of that period is found in the books of Ezra and Nehemiah, and one key point they make is the necessity of Jewish men to put away foreign wives (or not take foreign brides if unmarried) in order to preserve the authentic Jewish tradition. Against this stance, the author of Ruth tells the story of a young woman from Moab who marries a son of a Jewish settler in Moab, is widowed along with her sister-in-law and mother-in-law, goes to Judah when her mother-in-law returns there after out of loyalty to her and trust in her God, and ends up marrying a rich landowner and in consequence giving birth to the grandfather of none other than King David, who is conceived of as perhaps the ideal Jewish leader. The refutation of the Ezrahic stance on “marryin’ them furrin wimmen” is quite clear.
Much of the disputes among Christians about what the Bible really says can be resolved by simply reading it in context – what Paul called “rightly dividing Scripture.” Assertions based on an isolated verse, for example, may not be valid when you see what the text surrounding that verse suggests that it means, which may not be precisely what it appears to mean taken in isolation.