All three of these women are influenced by the opinions of others, and it is much to their detriment throughout the novels. Anne Elliot is influnced by her friend and mentor to not accept her sweetheart's proposals; her weak disposition and desire to please keep her from happiness for many years. Harriet is led on a wild-goose chase after a man who would never consider her for a bride, and it almost costs her the man who would consider her. She listened overly much to Emma's foolish meddling. Elizabeth, although she did have strong opinions based on her own experiences, relates when people call Darcy rude and cold. She is influenced by the liar Wickham to form false opinions about Darcy, that keep her from softening towards him for much of the novel.
All three of these characters learn their lesson about being too easily persuaded by others. They learn to go with their heart and their own instincts eventually. Another lesson that they share is that they learned they were not too good for their intended mates; that was part of the reason that they rejected them in the first place, because of a false sense of superiority.
Contrasts in the lessons learn stem from the source of their failures--Elizabeth was prejudiced, Anne was weak-willed, and Harriet was mislead. So, Elizabeth learned that though she claimed to be open-minded and accepting, she was more prejudiced than she would like to admit. Anne learned that she needed to trust her heart, even if it meant displeasing someone else. And Harriet learned that setting lofty goals is not necessarily the key to happiness. Their individual lessons fit the nuances of their individual storylines in all of their different ways.
I hope that those thoughts helped a bit; good luck!