It's difficult to comment on the accuracy of a work that runs to 10,000+ pages. I've only read (part of) The Age of Faith. It's very out of date. He's not a specialist in what he's writing about. He really likes pithy lines of analysis that seem archaic to me even for someone writing in 1950. And it's about as Eurocentric as you would expect for a series entitled The Story of Civilization the final six books of which only mention the rest of the world in passing, if at all.

He's a great writer, but I wouldn't read it for "accuracy".