I would be interested, Vladimir, in what developments would increase your probability that it is time for American LWers to exit the United States. In particular, how sharply would increases in racial tension and racial conflict increase that probability?

Honestly, this is one of the most difficult questions I've ever been asked! From my own experience, I can say that the scariest thing about outbreaks of mass violence is how hard it is to realize how bad the situation is getting until you're already in big trouble. I will try to answer your question to the best of my knowledge, though. (Since your question got strongly upvoted, I trust that my answer won’t be condemned for dealing with an overly political topic.)

For start, ethnic tensions and incidents are by themselves not necessarily a sign of impending social breakdown, even if there are significant local outbreaks of violence and mayhem. In the U.S., in particular, there have been periods of intense racial tensions and conflicts, some which caused fairly large casualties and wide-area devastation (like e.g. the 1967 riots in Detroit, Newark, and elsewhere, or the 1992 riots in LA). However, as bad as these were locally, they didn't lead to a larger-scale conflict and societal collapse on a nation-wide scale, since the higher levels of government (state/federal) have remained stable and in control.

For things to get really out of control, one of two things must happen: (1) a high level of government is taken over, legally or not, by people willing to start a civil, ethnic, or religious war or mass persecution, or (2) the authority of the government collapses, and the vacuum is filled by the strongest violent organizations that happen to be around (which will then typically proceed to go to war with each other and persecute whomever they don't like). It seems to me that neither possibility is likely with the U.S. in the foreseeable future (even though close things have happened with some of its local governments, which led to the aforementioned incidents). I’ll give the lists of some reasons why I believe this is so, and I’ll do this by way of contrast with the situation in ex-Yugoslavia:

Restraints on democracy. In ex-Yugoslavia, the post-communist elections offered genuine choice, in the sense that the collapse of the Communist Party’s authority created a situation where anyone was free to run on any platform whatsoever, and the winners, with popular support, would really have the power to steer things in whatever direction they wanted. In contrast, in the present U.S. system, elected politicians have little to no practical control over almost any area of policy, since whatever measures they want to undertake must pass through impenetrably thick layers of bureaucracy and over high obstacles of judicial review.
Of course, (1) is true only as long as the bureaucracies and the judiciary have real authority. However, I don’t see any signs of the state and (especially) federal authority in the U.S. weakening -- on the contrary, having some government agency, especially a federal one, get seriously angry at you for whatever reason is a frightful prospect for any individual or organization, and contempt of courts is unthinkable. In contrast, in ex-Yugoslavia in the late 1980s, it was evident that the communist authorities were starting to be seen as laughably impotent.
Political culture and tradition. In places where radical (and typically violent) regime changes are within living memory, government institutions are typically far less stable than in places where they reach far beyond that. The U.S. is certainly in the latter category, even if you count the Civil War as a radical regime change; in contrast, in ex-Yugoslavia, the regime was only 45 years old, with lots of people who were never truly reconciled to it and held (and perpetuated) grudges against it all along. This gives the U.S. government far more slack for blunders and mismanagement before its authority might start to get seriously eroded.
Ideological uniformity. The U.S. politics may seem ravaged by countless bitter controversies, but from a wider perspective, there is a remarkable ideological consensus with a very narrow (though, on most issues, slowly but constantly moving) Overton window. Only a small percentage of the population, and virtually nobody in the mainstream media, elite academia, and other influential sources of public opinion, hold any positions outside of it. In ex-Yugoslavia, the problem was primarily the ethnic rather than ideological conflict, so a better historical example of a country torn by truly deep ideological rifts might be the the Weimar Republic. Where such deep ideological rifts exist, of course, it’s hard to prevent political violence from becoming a regular part of the political struggle, and it’s unlikely that both the winners and the losers of political contests will accept its results peacefully.
Ethnic/religious identity politics. I wanted to compose a long paragraph about this very important issue, but then I realized it can’t be done without giving a lot of very controversial statements. So I’ll just make the general observation that in the U.S., there still exists a strong taboo against violence-threatening forms of identity politics at the higher levels of government, and in most places also at the local level. (The local exceptions to this rule have indeed led to instances of local violent societal collapse, as in the cities that were left ravaged and devastated by the ethnic/race riots and breakdown of public order some decades ago.)

(Besides these considerations, coups by security forces led by renegade elements in the government are another common source of violent political instability, but these are highly unlikely in the U.S., with its extremely strong tradition of lawful control over the armed forces.)

So, on the whole, I would start to get worried if I saw the following signs in the U.S.:

Weakening bureaucratic/judicial authority of the state and federal governments, especially the latter, which would enable elected politicians to exercise direct authority.
Loss of faith in the political institutions. By this I don’t mean the usual cynical and critical attitudes towards politics and politicians, i.e. when people think that they fall short of the official ideal, but a real loss of respect for that official ideal, thus opening the way for radical alternatives.
Erosion of the ideological uniformity, with radical positions starting to get taken seriously in the mainstream discourse, instead of being seen as loathsome extremism or charming but hopelessly naive idealism.
The principal lines of opposition in mainstream politics acquiring an ethnic dimension. By this I mean contests for public office where the candidates are primarily seen as representatives of conflicting ethnic groups, and such contests becoming the rule rather than an occasional local exception.

All of this still seems rather far-fetched in the present-day U.S., so on the whole, I don’t think exiting the U.S. for fear of violent social breakdown will be a rational step in the foreseeable future.

On the other hand, my view of the general direction in which the U.S. is moving is quite pessimistic, although I see a slow decay rather than a violent breakdown as the most likely course of events. Here I mean a continuing slow degradation of the quality of government, a gradual worsening of the present economic malaise, the life for most people getting uglier, more dysfunctional, and less dignified, the public intellectual life getting more mendacious and detached from reality, and so on. With this in mind, it may well be rational for many people to leave the U.S. (or move to a different place within the U.S.) in search of better opportunities. However, these are complicated issues, which would get us right into the middle of numerous controversies.