Peter Anson in his wonderful book Bishops at Large (which desperately needs reprinting) asked a very pertinent question. In the course of his book, he went into great detail about the proliferation of these little groups and noted that it was rarely sufficient for them to be episcopally consecrated only once: they were often consecrated over and over again by other bishops, as if this somehow made them even more valid. Anson asked: In what sense can these consecrations really be considered valid? Yes, of course, in a mechanical, pipeline, sense, all the bits are in place. But did our Lord really establish the college of bishops so that strange men might celebrate weird rites in odd clothes in their front rooms with their wives making the responses?
The older understanding of episcopacy would suggest that these episcopal consecrations lacked the essential element for validity—legitimate ecclesiastical authority. The Orthodox would agree. Whereas priesthood is sacramentally conferred by a validly consecrated bishop, episcopacy is [non-sacramentally?—in a literal sense] conferred by ecclesiastical authority unbinding the powers latent in the priesthood, so that the bishop thereafter exercises 'the fullness of the priesthood'. If there is no legitimate authority doing the unbinding, then the consecration would have no validity, no matter how many times the ceremony is repeated and, presumably, the specifically episcopal functions carried out by the recipient would, simply, lack validity. He would simply remain a presbyter (assuming he had received presbyteral orders from a bishop who genuinely possessed ecclesiastical sanction for his consecration).
This would sort out the proliferation of these strange sects who claim legitimate catholic status combined with arcane theological positions. And I hope it would bring to an end this rather disedifying scramble for episcopal orders. An Anglican priest in the Welsh borders told me that there is a not insignificant number of ordinary Anglican clergy who may well have obtained episcopal orders in anticipation of a melt-down of the CofE. Indeed he knows of one or two. Setting aside the question whether the CofE can count as legitimate ecclesiastical authority within the meaning of the term, the older theology would help them sort this one out. However, I am aware that the CofE is firmly wedded to the threefold ministry, and I rather suspect that this is where our more modern view came from in the first place!
Wikipedia makes the point that the episcopal consecrations of Archbishop Milingo were declared null, whereas those of Archibishop Lefebvre have been declared valid but illegal. This does rather suggest (probably, all other things being equal) that Rome is thinking about legitimate authority again.
If you have the stomach and patience for it, here is the lineage of one Episcopus Vagans (who delights in that nomenclature). He has his own blog.