What are at least four coincidences in Great Expectations which must be accepted by the reader in order for the story to be believed?
It is a coincidence that Molly is Estella's true mother.
It is a coincidence that the convict who Pip helped as a child is his true benefactor.
It is a coincidence that Orlick eventually works at the gate for Miss Havisham.
It is a coincidence that Magwitch turns out to be Estella's father.
It is a coincidence that Compeyson turns out to be the man that left Miss Havisham at the altar.
Look at all these people - they, just like Pip had GREAT EXPECTATIONS for life. Havisham wanted a successful marriage. Molly and Magwitch probably wanted to have children under good circumstances. Magwitch wanted to be a successful businessman. ALL OF THEM WERE LET DOWN. Thus, the GREAT, as in big or tremendous. Expectations are often hopes that never get met. They are ideas. They do not necessarily achieve purposes.
Pip always hopes for something more, even until the very end. As he finds Orlick at the door he feels like this man goes wherever he can to mess with Pip's life.
I think one of Dicken's purposes you can use is the fact that life doesn't always turn out the way we want. This is the lesson to take home for each of the characters mentioned above. When you take a look at the web woven for us, you see how closely linked all the manipulation was that made these people's hopes be nothing more than that, hope.
Warning: this essay has nothing to do with your question, but I can't resist making a comment.
Missy575 gives an excellent answer and lists some points I had missed.
Dickens actually wrote two endings to the story. In the original, Estelle marries a rich man who turns out to be a brute, who fortunately (for Estelle) dies. She marries a doctor of lmodest means. Pip meets Estell briefly as they pass in the street:
the lady and I looked sadly enough on one another . . .
and they never meet again.
In the later -- and probably better known -- ending, Pip and Estelle meet in a romatic setting. They walk out of the story, hand in hand, and Pip sees
no shadow of another parting from her.
There has been a good deal of discussion about which ending is "better" and why; see the reference below, if you have time to spare. I'm writing this because I think the original ending is far truer to the spirit of the book.