Can a Catholic priest take Anglican services?

As an Anglican priest and the Anglican Chaplain on the island of Ibiza I performed a marriage in Ibiza, for a Catholic couple. Their Catholic English parish priest in England completed all the necessary paperwork and authorities, petitioned their Diocesan Bishop of Durham who gave a dispensation for the couple to be married by me. This was sanctioned by the Vicar general of the Catholic Church in Ibiza and authority to take the wedding was conferred by the bishop of Ibiza. The couple were married by me in San Agustin and the marriage was recognised and validated by both denominations. I requested the presence of the parish priest of San Agustin, I was not required to do this, but he also signed their marriage licence. It was wise to do this but neither his presence nor his countersigning the licence was required. I guess my Holy Order were verified and line of Apostolic succession was valid.

I will add to brasshat’s answer the perspective of the Catholic Church.

As brasshat mentioned, the Catholic Church does not, in general, recognize the validity of Anglican Holy Orders (see Apostolicae curae, especially number 36), hence—unless a particular cleric can prove that he has obtained valid Holy Orders, say, from an Orthodox bishop—it must conclude that, in general, Anglican priests and bishops do not validly confect the Sacrament of the Eucharist. (In order to confect the Eucharist, one must possess at least the rank of presbyter.)

For that reason alone, it would be gravely illicit for a Cathlic priest to take on an Anglican service, especially since Anglicans have a wide diversity in opinion regarding the nature of Holy Orders and the Eucharist.

In any case, even if the Anglican Church had valid Holy Orders, at present it exists in a state of schism with the Catholic Church, and Canon Law explicitly prohibits communicatio in sacris; that is, participation in sacred rites of a group not in communion with the Catholic Church:

Can. 1365 A person guilty of prohibited participation in sacred rites (communicatio in sacris) is to be punished with a just penalty.

It is entirely possible, of course, for a Catholic priest to leave the Catholic Church and enroll in the Anglican Church—but such an action is not, from the Catholic Church’s point of view, licit or laudable. (For example, if he wished to return to the Catholic Church, he would probably not be allowed to resume his priestly ministry.)

There are three things which are necessary for a sacrament to be valid. The form, the matter, and the intent. I once heard a priest say that he could come riding into the Church naked, on an elephant, and so long as he had unleavened bread and wine, said the mass using the right words, and intended for the Mass to be valid, it would be.

Having read the Book of Common Prayer's rubrics, if RC priest intended to use them for Mass, that is, I believe, sufficient for it to actually be a Mass. It would be valid but illicit. He might receive a sternly worded letter from the Bishop. Maybe. (I know of one parish which largely re-wrote much of the Mass to make it rhyme (!), they did it for years before the bishop told them to stop).

As to "leading a Protestant service", if a priest is intending to confect the Eucharist, then is it Protestant? On the other hand, if the priest is not intending to have it be a Mass and there is still communion, or the priest tries to use illicit matter (coke instead of wine, wonder bread instead of unleavened), that would be a much more serious offense.

It also might be noted that ordination is something permanent. It cannot be undone. Even a defrocked priest has the ability to say Mass, but it is a sin to do so (in most circumstance). So the question really is a matter of what the priests intention is.

The churches of the Anglican Communion recognize the validity of Holy orders conferred by the Roman Catholic Church, so that a Bishop, Priest or Deacon who converted from Catholicism to Anglicanism, would remain a Bishop, Priest or Deacon, and could serve in the appropriate roles in the Anglican Church, subject to the relevant canon(s) of the various constituent churches of the Communion. It is also probably true, that a Catholic Bishop, Priest, or Deacon could be permitted to exercise his role in an Anglican church on a one time basis. In either case, though, whether a full conversion or a one time event, this would violate Roman Catholic canon law, and the Catholic Priest, Bishop, or Deacon, would likely be automatically excommunicated by virtue of having performed the act.

As far as going the other way, the Roman Catholic Church recognizes Anglican orders as "absolutely null and utterly void" (Pope Leo XIII's Apostolicae Curae §36), so an Anglican converting to Catholicism would have to be ordained in the Catholic Church. This does, in fact, happen, and there are some number of Anglican clergy who have converted and been ordained and who serve as Priests in Roman Catholic environments, even when those Priests are married.