The narrator says that Widow Wycherly had been very beautiful when she was younger. But she lived in seclusion on account of gossip and scandalous stories which made the gentry (people of a higher class) want nothing to do with her. Her promiscuous behavior led to a bad reputation and missed opportunities for marriage and social advantages. Also, in the wake of this, because she hid herself from others, she missed an opportunity to refute these scandalous stories. Or, if the stories were untrue, she missed an opportunity to challenge the gentry and perhaps win back their approval. But even if the gentry never again accepted her, she missed the opportunity to befriend the lower classes. In hiding, she prevented any opportunity to interact with, or even marry, someone of any class.
In the end, she (as well as Colonel Killigrew and Mr. Gascoigne) misses an opportunity to learn a lesson. She has not learned, from experience, that beauty is fleeting and superficial. She has not learned that her vice for vanity is selfish and illustrates a flaw in her character. Also, if those scandalous stories of her younger days are true, she has not learned that flirtatious behavior will not lead to winning the respect of others. When she is initially transformed into a younger woman, she thrives on flirting with the other men. Isn't this what allegedly garnered her a bad reputation? Killigrew and Gascoigne are equally dense in missing the opportunity to learn similar lessons in their lives and via this experiment.
Note that the experiment seems to be whether or not they will become young again. But from Dr. Heidegger's perspective, the experiment is also a study about how and if these three guinea pigs will learn anything in the realm of wisdom.