In his letter, Dr King states that “Injustice anywhere is a threat to justice everywhere.” In your opinion, are there current examples of this to be found?
Countries that serve unjustly their own citizens certainly are a tremendous threat to people who are arrested in their country. For instance, a former United States CIA agent (and Jewish) who has been held prisoner in Iran is probably not faring well as a prisoner of this country that is infamous for its hatred of both the US and Israel.
This is a highly subjective question because we have to guess to determine whether a specific injustice (many of which exist in the world) is a threat to justice everywhere. There is no way of proving it one way or another.
One example of injustice threatening justice could perhaps be seen in the rise of China. China does not really care about human rights within its own country. As it becomes more powerful, it deals with other countries and does not push them (as the US and its allies sometimes do) to improve their records on human rights. Thus, injustice within China can be said to threaten the chances for justice in other countries.
Within the US, you can claim (depending on your political ideas) that discrimination against gay people threatens everyone else. You could argue that a society that tolerates that sort of discrimination might also tolerate other sorts. From that point of view, anti-gay discrimination is like a germ that threatens to make our whole society sick. The presence of that kind of discrimination makes other kinds more likely to happen because it makes us more likely to accept other forms of discrimination.