What is the integrity of The Valley of Fear?

I'm not sure what you are referring to in terms of integrity, but one of the most compelling parts of the Holmes stories is the relationship between Holmes and Watson. If this is the only Holmes story readers have ever read, then it still does an excellent job at portraying the relationship and demonstrating how both men benefit from it. Watson's faith in Holmes's abilities is ever-apparent here, as it is in other stories. Holmes's ideas occasionally seem wild or impossible, but Holmes always gives his friend credit. Watson's faith may be tested but it never falters; this is the recipe for not only a good friendship but also a dynamic detective duo.