In the context of this text, how has America changed over time? To what extent do you see the problems that King describes in this letter in society today?

This is only a short answer space and your question is pretty complex. It also depends on your opinion. I'm sure race relations have progressed since King wrote his letter but I'm not sure by how much. I'm not an expert on race-relations but racial inequality still feels rampant in the United States. Schools, neighbourhoods, healthcare still seems pretty segregated: not by laws but by socio-economic demographics. I think the United States still has a long way to go to realize King's dream.