I think that one of the more serious aspects of Wharton's work is its study of human cruelty. While one might make light of the pettiness displayed between Grace and Alida, there is a undercurrent of cruelty in how they wish to exact revenge on one another. Their friendship or association features this streak of cruelty underneath. There is little in way of mercy or temperance in their relationship. It is predicated on one seeking to outdo the other. Like two aged gladiators fighting in the twilight of their careers, both seek to land the crippling blow one after another. Of course, Grace's disclosure at the end of the story is the most crippling of blows to Alida. Yet, the entire emotional swordplay between both reveals how rivalry and cruelty enter even the most conventional of friendships. The study of human cruelty is one of the more serious aspects in Wharton's work.
I think that another serious aspect of the work is how flawed the belief in one's own superiority can be. Alida is of the mindset that she is superior to Grace. She opens the proverbial can of worms by seeking to exact her own superiority. Thinking that she has understands everything and cannot be surprised by anything, she forgoes caution and even human decency in wanting to display superiority to Grace. The flawed element of her logic is evident in Grace's disclosure, something that would fundamentally shatter Alida's sense of superiority. I think that Wharton's exploration of this condition of human beings is a serious effort. The idea of proceeding with life without humility can end up being a disastrous endeavor.