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.)