We're a self directed team. And like everything else, it has it's ups and downs. On the plus side, we don't have any managers. On the minus side, it turns out that managers do a lot of useful things and someone has to do them. And without managers that someone is us.
A self directed team is half benevolent dictatorship and half democracy. It allows ideas and opinions to flow up from the bottom without layers of managers filtering them. It also allows information to flow down from the top without layers of managerment re-interpreting it. Both of these are good things, and are traditionally where top down management has it's problems.
A flat organization is like a hyperlinked internet a lot more than it's like a heirarchy. While any particular individual may not know the answer to a particular problem, they will know where to go to get that answer. The larger the orgaization the more hops it takes to get there, but it's a lot quicker than navigating a heirarchy, especially since people who need to work togther naturally form their own informal links. The people are capable of taking responsibilty. They may need training, but that's because they're tasked with doing jobs managers are traditionally trained to do. As a result you end up with a much more fluid organization and changes within the organization don't produce a lot of instability.
For example, it could be assumed that we reorganize, at a minimum, every six months. In truth we reorganize a lot more frequently than that. But since we can effectivly reorganize very quickly and without the chaos that normally follows a reorganization, we usually don't notice that it's occurred.