Alternatively, this question could be phrased "What items within the Vatican archives are restricted to the public that we know about? Are there any items that the Vatican is rumored to have which would carry great significance?"
If you are referring to the Vatican's "Secret" Archives, I'm afraid you might be disappointed. Secret, in this case, means private or personal. Access to items in the archive over 75 years old are available to researchers from universities or other similar organizations. A few exceptions have been made to the 75 year rule, but it is otherwise firm. Like any archive, access to rare or delicate documents might be limited, or you might have to use a facsimile document. The documents are not restricted because of content. Several of my colleagues have accessed the Vatican Secret Archives for research.
If you were already aware of all that, then generally the only people who would benefit from research to the Vatican's archives closed records would be those interested in documents they created or stored since 1939.