Why did florida oreder a recount of 2000 votes

A simple answer to your question is:
Al Gore didn't believe the state has run a fair election

An informal structure in a bureaucracy would be something like so-called "office politics". where there's a formal structure set up for the organization, but then an informal subculture as well that has a way of organizing the bureaucracy further. this can be positive because it sets up an added degree of organization, albeit informal, within the bureaucracy.