What evidence would convince you that your worldview is incorrect?

There are two different categories of such evidence: those that would convince me a god existed, and those that would not convince me a god existed but that something supernatural existed.

As to the former, I have already answered that question here (look on this website for the question "What kind of evidence could convince you that there is a god -- like an omnipotent type god, such as in Islam or Christianity?" which is listed under questions asked of the atheist correspondent).

As to the latter, I have already answered that question elsewhere. See...

Defining the Supernatural