Brigham Young offered this instruction in the spring of 1844:
If a man preaches anything in error, pray to God that no man may remember it any more. No Elder will correct another in public before unbelievers unless he has the sinking principle. I call all the Elders together to witness that I always use charity, for it covers a multitude of sins. Let us obey the proclamation of Joseph Smith concerning the Elders going forth into the vineyard- to build up the Temple- get their endowments
The “sinking principle” was explained by Brigham as follows:
the speech and conduct of Elders, one towards another — one Elder will speak evil of another and when you undertake to trample on another you will sink yourself. [such] a man has [the] sinking principle 
Brigham’s advice about criticism is pretty much a deeply embedded principle in the modern Church. But how far does it go, or, how far should it go? When a person in a responsible position (stake president) has reliable information to the effect that another officer (bishop) is in some form of error (say, this bishop displays overtly lustful attitudes toward certain members of his congregation – not directly, but in conversion with a counselor who reports these repeated conversations). The SP speaks to the bishop, but the behavior continues and no further action is taken.
When the Mormon Doctrine snafu took place, one of the major concerns over the first edition was the effect a public Church rejection of the volume might have on its author’s credibility and ability to function (that was clearly a higher priority than whatever doctrinal speculations or errors were in the book). It’s pretty clear that the bar for public criticism let alone discipline of general Church officers is a high one. But one guesses that this is not exclusively about the individuals involved. How important is it to the health of the Church that the foibles of its members or more especially its leaders remain private or at least uncelebrated? And where is the threshold for violation of that social compact?
I won’t comment on the recent storm over President Boyd K. Packer’s remarks and the subsequent changes in those remarks except to say it wasn’t the first time such things have happened.
Antebellum American Protestant religious organs show that public criticism of preachers over doctrine (the “wrong” atonement theory, say) was not unknown by any stretch but that is less common now. Brigham Young himself publicly reigned in Orson Pratt over doctrinal differences. The threshold for such action may be different now however. On the other hand, the correlation movement and its corollaries control some speech seemingly at even the highest levels. If indeed the bar is higher for public criticism in the Church, does this effect the nature of private correction? I think it might.
 General Church Minute file, 9 April 1844, holograph, Thomas Bullock. CHL.
 Public criticism of allies is nearly always regarded as uncouth to a point. But the “Reagan dictum” appears in any number of religious contexts, not just Mormonism. Think Roman Catholic leadership treatment of pedophile priests.
 Consider for example the excommunication of Elder Richard R. Lyman for adultery.
 See Spencer W. Kimball’s rejection of Brigham Young’s ideas.
 Joseph Smith was not shy about correcting colleagues in public on occasion.