Some might suggest 'never'. It's impolite to chastise others, after all. Better just to mind one's own business, live and let live, etc.
As stated, this categorical denial is surely too strong: we shouldn't just "turn a blind eye" if our associates engage in acts of cruelty or bullying, for example. The social enforcement of (at least some) moral norms seems essential for maintaining a decent society, especially given that not everything bad can be legally prohibited. So some moral failings, at least, may be other people's business. The question is where to draw the line. (I tend to favour more confrontation than most people, at least in theory, but that's probably due to my optimism about how constructive disagreement can be.)
At the other extreme, one might argue that wrongdoing is always others' concern (at least in principle): that's just what makes something a moral - rather than merely personal - failing. Here we need to clarify whether we mean it is the business of some or all others -- only the former seems plausible to me. But in any case, it doesn't follow that the appropriate way to respect this concern is always to voice it.
Note that it would seem ridiculous to actively seek out people to remonstrate. And even if I accidentally happen across a forum of noxious homophobes, or a news story about some evil dictator on the other side of the globe, it may not seem worth engaging my reactive attitudes. Although their blameworthiness renders them fitting or legitimate targets for censure, some further, practical reason is arguably required to make it actually worth doing.
This suggests two key factors: the importance of the violated norm, and the likely efficacy of our remonstrations -- whether at convincing the wrongdoer to repent, or strengthening the norm for others in our moral community. This latter goal suggests that our affiliations (if any) with the violator may strengthen the case for public censure, in hopes of counteracting the human tendency to show less respect for norms that others in their "group" have violated. (On the other hand, increased exposure may prove counterproductive for the same reason.) In any case, some kind of 'division of moral labour' may be appealed to here also: it'll generally be easiest if groups police their own -- not to mention more effective, as we're generally more responsive to the opinions of people "like us". (Widespread non-compliance renders this an imperfect rule, however.)
I also feel like more prominent, well-respected, or influential people ought to be subject to increased "vetting" and criticism. I guess it does more good to counteract the influence, so far as we can, of those that actually have some in the first place. They might also serve as evidence that a view is more widespread than we'd realized.
For example, it's one thing for nationalistic wingnuts to blithely disregard the interests of the global poor, but it's something else altogether to see Richard Posner advocating that foreign aid "that goes to fight malaria... or promote agriculture or family planning there could be redirected [in part]... to the United States to help get us out of our economic predicament". He chillingly concludes:
I grant that poor countries may be harder hit by what is a global depression than the United States, but I consider Americans' obligations to be primarily to Americans rather than to the inhabitants, however worthy, of foreign countries. I am also inclined to think that charitable giving abroad is so closely entwined with the nation's foreign policy objectives that it should be regulated by the State Department rather than left entirely to private choice.
But I digress. Any other suggestions regarding when censure is called for? (I guess in practice we can generally just follow our inclinations here, as in most matters, but they might always be refined. Besides, I'm curious.)