I'm a software developer and work for a company that operates this way: no official managers, just 1 owner and flat structure otherwise. There are about 90 of us and it's scaled well so far, but we'll see how the future goes.
I was skeptical when deciding to take this job and still see flaws in it, but then again... there were plenty of flaws at my previous job with a traditional corporation in the same industry as well. One interesting thing is that leadership/un-official hierarchy does emerge: if someone has been working on a product or in an area for a long time and becomes an expert there, he becomes a de-facto leader whom other people look to for guidance. The most important thing for companies who want to avoid traditional management structures is good hiring.. you have to hire people who are pro-active and don't need someone to tell them what to do, and this is very difficult.
BTW, side note: my company is quite Mustachian in other ways: we are distributed/ work from home (though I happen to live near the office so I come in often), have higher-than-market salaries, but no fancy benefits and a VERY spare office. Everyone can buy whatever he or she needs for work (equipment, software, etc) with the company card, remote employees can travel to the office whenever they want, and there's no vacation policy or set hours. (Sometimes I think this actually makes us work *more* than in a traditional 9-5 office job with x weeks of vacation, though!)