The problem with replacing the term "black" with "African-American
" is that not all people who consider themselves black are African-American.
I witnessed an instance of this first-hand, when, in an attempt to be politically correct, a woman standing near me asked someone: "Who is that African-American gentleman who's speaking?" To which the other person replied, "He's not African, he's Haitian." But he still considered himself "black."
Therefore, rather than use the word "African-American" as a cure-all for the so-called "slur" of calling someone black, people should realize that everyone needs to have some kind of label applied to them, otherwise it would be impossible to distinguish one person from anyone else (Even the term "person" is a label, differentiating a human being from another piece of matter).
Perhaps for the sake of sanity, the terminology for describing someone previously referred to as "black," "white," "brown," "pink," whatever should be altered so as to describe explicitly the person's skin-color, rather than their race or their personality (i.e., to identify someone who looks “white,” one could say "that guy with light skin," instead of "that white guy"). Of course it's all relative, but I think you'll find it's much less problematic than trying to find a simple definition for a person based on their skin color.