All and all it is a non trivial problem. You have at the very least have to attach some kind of form of reputation system into the verification process. Even with that you will still have the "misunderstood genius" issue, or the "excellent reputation professor" that everyone trust without (enough) verification.
But at least there’s be a system for other researchers to record “failed to replicate” that could give a channel to critique reputable professors that’s not controlled by the same professors (as they often can in journals).