I do not believe in the idea of partial communion, but what is a good explanation of this quote of St. Leo I?:

Quote

Letter 159 of VII. About those who in fear or by mistake were re-baptized.

"But as to those about whom you thought, beloved, we ought likewise to be consulted who were either forced by fear or led by mistake to repeat their baptism, and now understand that they acted contrary to the ordinances of the Catholic Faith, such moderation must be observed towards them that they be received into full communion with us, but not without the healing of penitence and the imposition of the bishop's hands, the length of the penance (with due regard to moderation) being left to your judgment, as you shall perceive the minds of the penitents to be disposed: in which you must not forget to consider old age, illness, and other risks. For if a man be in so dangerous a case that his life is despaired of, while he is still under penance, he should receive the gracious aid of communion by the priest's tender care."

http://ww.newadvent.org/fathers/3604159.htm

9. The Church, founded on these principles and mindful of her office, has done nothing with greater zeal and endeavour than she has displayed in guarding the integrity of the faith. Hence she regarded as rebels and expelled from the ranks of her children all who held beliefs on any point of doctrine different from her own. The Arians, the Montanists, the Novatians, the Quartodecimans, the Eutychians, did not certainly reject all Catholic doctrine: they abandoned only a certain portion of it. Still who does not know that they were declared heretics and banished from the bosom of the Church? In like manner were condemned all authors of heretical tenets who followed them in subsequent ages. "There can be nothing more dangerous than those heretics who admit nearly the whole cycle of doctrine, and yet by one word, as with a drop of poison, infect the real and simple faith taught by our Lord and handed down by Apostolic tradition" (Auctor Tract. de Fide Orthodoxa contra Arianos).

The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium. Epiphanius, Augustine, Theodore :, drew up a long list of the heresies of their times. St. Augustine notes that other heresies may spring up, to a single one of which, should any one give his assent, he is by the very fact cut off from Catholic unity. "No one who merely disbelieves in all (these heresies) can for that reason regard himself as a Catholic or call himself one. For there may be or may arise some other heresies, which are not set out in this work of ours, and, if any one holds to one single one of these he is not a Catholic" (S. Augustinus, De Haeresibus, n. 88).

The need of this divinely instituted means for the preservation of unity, about which we speak is urged by St. Paul in his epistle to the Ephesians. In this he first admonishes them to preserve with every care concord of minds: "Solicitous to keep the unity of the Spirit in the bond of peace" (Eph. iv., 3, et seq.). And as souls cannot be perfectly united in charity unless minds agree in faith, he wishes all to hold the same faith: "One Lord, one faith," and this so perfectly one as to prevent all danger of error: "that henceforth we be no more children, tossed to and fro, and carried about with every wind of doctrine by the wickedness of men, by cunning craftiness, by which they lie in wait to deceive" (Eph. iv., 14): and this he teaches is to be observed, not for a time only—"but until we all meet in the unity of faith...unto the measure of the age of the fullness of Christ" (13). But, in what has Christ placed the primary principle, and the means of preserving this unity? In that—"He gave some Apostles—and other some pastors and doctors, for the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ" (11-12).