Falkner uses his extraordinary art to describe a world dying of old age, with us gasping and choking in it.What are two parts of the story that show this is true?
I think the first part of your statement is true, that Faulkner does indeed show a world that is desperately trying to hold on to a traditional (and outdated) vision of progress. However, if when you say "us," you mean the audience, I have to disagree that "we" are gasping and choking in this world. Such an image suggests the audience is as ignorant to progress as the characters or stuck in the same world, neither of which is true. Part of the beauty of "A Rose for Emily" is the pity evoked in a sympathetic audience for the principle character, who is the victim of a society that is unwilling to change.
Two parts of the story that illustrate a world "dying of old age" would include descriptions of Emily's very traditional and overbearing father. It seems she is destined to become a spinster because her own father refuses to let her grow up. Later, when Miss Emily takes a keen interest in Homer Baron, the town is unwilling to support her courage in pursuing this friendship because Homer is a "Northerner," a "day laborer," and likely interested in men more than women.
The progressive audience that is reading the story today, sympathizes for Emily and looks at her father and the citizens of the town (characterized by the narrator) as the most ignorant. The audience is not stuck in this society as Miss Emily is. Therefore, we wish we had the power to lead her out.