Enotes provides a wonderful link to themes, which I have included below, but I will address your question briefly to get you started.
The most powerful theme in Twain's story - as in many of his stories - is hypocrisy. The town swears to be "morally upright and unfailingly honest". However, as soon as the gold arrives, suspicion and fear dominant. If everyone is so holy, why would there be suspicion? Also, the town is known to speak ill of their neighbors while behind close doors, to gossip and debate who is the most hated. However, they do not show this face out on the street. Duplicity abounds, despite what the town shows on the surface.
Greed can certainly be one of the themes. If the gold creates suspicion, there must be an element of greed in the town. Mary wants to keep the money and fears others will take it. In a less literal sense, the desire to be less hated than your neighbors is a form of greed - greed for attention and for status. When Edward conceals his part in the scandal, he does so to protect his image - he is greedy to always be thought of as "moral".