Does Fr. Gravel really have permission to hold office?
Under the 1983 Code, Catholic priests are flatly prohibited from holding governmental office: Canon 285.3 plainly states "Clerics are forbidden to assume public offices which entail a participation in the exercise of civil power." The legislative history of this norm makes obvious the Legislator's intent to eliminiate any exceptions to this rule. See Peters, Incrementa in Progressu at 234.
Unlike those situations where a priest might be given permission to serve as an agent for lay persons or as co-signer of a loan, or to hold office in unions or political parties (see 1983 CIC 285.4 and 287.2), there is no provision in Canon 285 for bishops to grant a priest permission to hold governmental office. None. Presbyteral council "approval" of any alleged "permission" is completely irrelevant.
The Holy See could, of course, grant permission for a priest hold governmental office, but there is not the slightest chance that Rome would do anything to enable this cleric to spread his kind of scandal at the national level.
Prescinding from other canonically confusing aspects of this case, the only theory by which Fr. Gravel might have been given episcopal permission to seek national office would be in virtue of a dispensation from disciplinary law under 1983 CIC 87 and 90. The standard canonical authors recognize such a possibility, but when commenting specifically on the prohibition against priests holding major governmental office, they stress how low is the likelihood that such permission would ever "contribute to the spiritual good" of those under a bishop's care. In Fr. Gravel's case, of course, the assertion that such permission might serve a "spiritual good" would be laughable.
In short, it seems that someone has either thoroughly confused Canon 285 with Canon 287, or has deeply disregarded Canons 87 and 90. Either way, this situation needs correction.
(A minor clarification on the LSN report: the canonical prohibition against priests holding governmental office did not start with the Drinan case in the USA; it was part of the Pio-Benedictine Code (see 1917 CIC 139), though Fr. Drinan's conduct in office through the 1970s certainly helped galvanize renewed enforcement of the norm.)
Same Day Update: Another Canadian priest, Fr. Thomas Dowd, writes that Fr. Gravel's "permission" to hold secular office was contingent upon his accepting certain restrictions on his ministry. Those restrictions seem like some of the "other canonically confusing aspects of this case" I referred to above. Interesting, but it doesn't change my analysis. There are no conditions upon which episcopal "permission" to hold governmental office can be given to a priest. Again, if this is not a dispensation case, as doubtfully valid as that dispensation would be, it's nothing.
Updates, November 1: Skimming some other comboxes on this topic, I see some folks confusing deacons and priests here. Please note, permanent deacons, per 1983 CIC 288, are not included under the c. 285 prohibition at all. Technically, they are not an exception to the rule; they simply don't fall under it to begin with. It is therefore confusing for some to be asserting that permanent deacons can hold secular office "if they have their bishop's permission". Per the Code, permanent deacons don't need permission at all, since they are not prohibited in the first place.
BTW, I provide canon numbers in my posts precisely so people can look up these things themselves. But too many folks don't do that before posting what they think are corrections.
A French-language communique from the Diocese of Joliette, citing no canons, asserts that Fr. Gravel has episcopal approval to run for civil office on condition that he basically lays aside priestly ministry for the time of his political activity. (Translation of communique and pointed questions from CWN here.) Whatever else may be said about Fr. Gravel's overall situation, I see no basis in canon law for this sort of "compromise".
Update, November 2: Jimmy Akin is predicting that Rome will intervene and order Fr. Gravel to stand down. This seems, indeed, the last hope that the Catholic Church in Canada will be spared its version of the Drinan disaster.
Update, November 14: There's now another one in Toronto. I can only say again, I see no basis in canon law for granting "permission with conditions" in these cases. For priests to hold governmental office requires dispensation, or it is canonically illegal. That is not a verbal quibble on my part. The character of "permission" differs in several respects from that of "dispensation" and, if history is any guide here, instances of misapplied canon law usually tend to get worse, not better, over time.