What is Faulkner trying to show about traditional (old) southern values by having the town discover Emily’s insanity?
I don't think it is southern values that Faulkner is exposing as much as the reluctance to face reality. Although Dixie Carter once said on "Designing Women" that all southern people have crazy relatives that we love to show off, it is not particularly southern to be insane. The story could just as well have been set in Maine (minus a few elements).
The story does have conflict between the old ways and the modern way. The old way was to overlook Emily's nonpayment of taxes or to sneak at night to clean up her yard. The old way was for a man and woman who spent any time together alone to eventually marry. The new way was completely foreign to Emily.
My question is: Was she really insane?
Think of Emily's dark secrets -- which existed under the veil of aristocracy -- as an allegory for the ugliness that existed in the antebellum South. The was "hidden" by the idea of the idea of the southern aristocrat/gentleman and in idyllic portraits of southern life; only after it crumbled was its true horror exposed.