Suppose a mad engineer needs the world destroyed by next Tuesday. For efficiency's sake, he considers "Gray Goo," a hypothetical end-of-the-world scenario in which self-replicating machines devour the entire planet while building more of themselves. 

Realistically, what would be required (in terms of technology, resources, schedule, etc) to successfully transform the planet into all-consuming nanomachine?

Ethics aside, what are the fundamental flaws of the Gray Goo scenario?

This is not so much a question on how to write a believable Gray Goo disaster as a reality check of the concept itself. 

(I may be inspired to resume my mad-science degree this turns out to be feasible, so please do your best to dissuade me today :) )