I recently learned that, in 1763, John Wesley was consecrated a bishop by Erasmus of Arcadia, an eastern bishop who was visiting London. A number of Methodist ministers were also ordained priests by Erasmus. This means that Methodist ministers have authentic apostolic succession. Can we then not consider both the ministerial authority and the sacraments of the Methodist Church to be licit expressions of catholic order?
I think I would be curious to know what firsthand evidence we have. Who is this Erasmus, a valid bishop and if so was he disciplined for the usurpation of the metropolitan authority of Canterbury? From the little I know of John Wesley's clerical status, it was clear to me that he followed the presbyterian path in ordaining other priests while a priest himself
The legitimacy of Erasmus of Arcadia is extremely murky and I don't think it will be possible to settle the question either way. Wesley was trying to cope with what he considered to be a dire emergency and would have preferred to do things the normal way. He justified the practice of presbyters raising bishops using a number of precedents from ancient church history, particularly the Alexandrian practice. It's true that in the ancient church sometimes bishops were elevated by councils of presbyters or even by popular acclamation. Whether this justifies Wesley consecrating bishops in the 18th century is a question I leave to others.
I'm not even sure it's safe to say that Erasmus ever ordained Wesley or any of his colleagues to the Episcopacy, just the Presbyterate, and I don't think Wesley ever considered ordination by him. If I remember correctly, he opposed all but one of the ordinations, on the grounds that they did not understand the language they were conducted in (the first one did, IIRC). That's a pretty piecemeal regurgitation of something I read somewhere, I guess.