Brown's view, and that of a good many, is that the inspiration of the Scriptures has the effect of rendering Scripture inerrant when relevant to human salvation.
This seems a little peculiar. As if the Almighty had only so much inerrancy to go around, and so saved it for the really important bits.
The other thing that strikes me about this doctrine is that it's precisely the most important bits that are most obscure. If we want to know how many camels Job owned, that's easy, anyone can tell you that. Ask people how many Persons there are in the Godhead and they start chopping each other's heads off and sticking spikes into one another, there being apparently no other way to settle the question.
Arius or Athanasius? Faith or works? How many sacraments are there? Should I be Monophysite, Nestorian, or Chalcedonian? Transubstantiation or consubstantion? And, as you candidly point out, it is equally difficult to find out what the important things are.
And yet
this is supposedly what God lavished extra care on.
Fortunately, we
can all agree that Job owned three thousand camels. One wonders what he did with them all.