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You are correct when you say that this is a timeless piece of writing that is as true today as it was when Jane Austen wrote it.
If one is trying to find situations which provide dissatisfaction, one need only look to the news and the "institutions" of our society. Politics provides this sense of dissatisfaction, as does the Catholic church. These problems stem directly from the inconsistency of human characters.
The ideal of the Constitution and its service to society has been lost in the bickering between parties by both sides to obtain the upper hand. Even legislation with the best of intentions gets mired down and rejected because of personal political agendas. Sadly, the same is true of the Catholic church. Those trying to do good for their faith lose heart in the the tragic inconsistency of others who have promised to serve God and man.
These are only two examples: we see the irony of the promise vs. the reality in every profession. Truthfully, though, I see it as a part of the human condition. Mankind is imperfect and so we are imperfect. The sense of "little dependence can be placed on the appearance of merit or sense" is directly associated with the ability people have to appear one way and act another. What we see is not always what we get, unfortunately.
However, I also believe that in light of this statement, and the sad realization that comes with it, Austen was also able to see the goodness in others and have a hope in the sensibilities of others who attempted to rise above the common dealings of man, to choose a different path and follow a higher purpose.