I took a class using the Moore method during my freshman year as an undergraduate (back in 1998). I really enjoyed it, but now that I've acquired a bit more teaching experience I think the following points should be made. I should remark that I've never tried teaching a course using this method myself.
Like Felipe said, it is not good for conveying a lot of information. It is more of an ``experience''. It is thus best for classes like baby-Rudin style analysis classes in which there are few hard theorems and not too much that HAS to be covered.
It is important that the class is small and that the experience/talent levels of the students are relatively equal.
I think that such classes can be valuable to a certain kind of student (one who is relatively strong already and who enjoys competition), but I don't think it should be mandatory. Maybe one section out of a multi-section class.
I want to elaborate a bit on the third point. I think the stereotype of mathematicians as aggressive and hyper-competitive is a dangerous one, and has the effect of discouraging students who do not fit that stereotype. It is important that when a course like this is offered, an effort is made to clarify that not all students need to take it. I could envision a culture developing where the Moore method section has a reputation as being the "real section" for the "best students". The faculty need to make a serious effort to prevent this from happening.