The resignation of Benedict XVI portends no problems for Church governance.
We know exactly when the vacancy in the Apostolic See will occur (2 pm, Eastern time, Thursday, FEB 28) and we know what laws will govern the Church during said vacancy (ap. con. Universi Dominici Gregis). Up until then the pope is fully the pope (c. 331), and after that, he isn’t; most heads of Roman dicasteries will immediately cease functioning in their offices, and canonical clocks will start ticking, culminating in the next papal conclave in mid-March.
What canon law does not, to my knowledge, treat of—and has not experienced for nearly 600 years—is the status of a former pope. I’m sure Vatican protocol experts are working on it, but my ruminations are as follows. These are, per force, first impressions.
Resignation in canon law impacts only the offices actually resigned. Benedict XVI is resigning the distinguishable but inseparable offices of the papacy and the bishopric of Rome, so, effective the evening of February 28, he will hold neither office (nor of necessity the papal Lateran basilica).
Now, prior to his election as pope in 2005, Joseph Ratzinger was a cardinal in the Roman Church and possessed certain rights and duties as a cardinal. I am not aware that he resigned that office (though he vacated his suburbicarian see of Velletri-Segni, which is now held by Cdl Arinze), so, I am thinking that, upon resigning the papacy, Benedict XVI simply resumes his place among the College of Cardinals, having never left it, and of course, would be a regular member of the College of Bishops (c. 336).
If the pope simply resumes his status as cardinal, a number of sticky problems are avoided: for example, he automatically falls under the exclusive jurisdiction of the next pope (c. 1405 § 1, 2º), and he would likewise enjoy faculties for sacramental confession everywhere (c. 967 § 1). Could we really imagine the alternative: a former pope being subjected to the jurisdiction of someone other than the next pope, or his needing faculties from an ordinary to hear confessions? Well, if Benedict is not a cardinal come the evening of Feb 28—well in advance of the arrival of new pope who could take whatever action he wished at that time—both of those scenarios would seem to apply.
Also, upon acceptance of the office of Bishop of Rome, I think the pope became incardinated in that local Church (cc. 265 ff); now, I see no mechanism by which a bishop loses his incardination upon resigning his governing office, so it seems that Cdl. Ratzinger would remain a cleric of the Archdiocese of Rome, being generally bound by the rules applying to all such clerics. He would be the emeritus bishop of that local Church (c. 185). An expert in Italian canon law could tell us whether retired prelates there are voting members of the Italian Episcopal Conference (c. 454 § 2), but, aside from his being accountable only to the future pope, I think it is clear that Benendict intends a life of quiet prayer and study, so the question is interesting (I think!), but quite moot.
It is customary in some places to refer to former presidents and former ambassadors as “President” or “Ambassador” after they have given up office. I see no problem in referring to “His Holiness, Joseph Ratzinger, Papa Emeritus and Cardinal of the H. R. C.”
See also: When will the conclave start?