Among the major themes in the novel, one of the most interesting to analyze is the ambiguity with which Hawthorne narrates many of the major events. Ambiguity, as a theme, touches upon a lot of the issues in the novel.
One of the ways that Hawthorne uses ambiguity is in the description and actions of Dimmesdale. While the narrative is focalized through the emotions of Hester Prynne, Dimmesdale remains in the back. Even his name embodies the nature of his gradual "dimming" in the story until the moment of this death. His once dashing personality has been weakened by the sin that he hides, and which he had to witness Hester pay for by herself. Hence, the name "Dimmesdale" is a symbol of the ambiguous man who we never get to meet entirely.
Ambiguity is also seen in the way in which the townspeople view Governor Bellingham (whose last name also symbolic of an opulent, thick, fat, and superfluous man) lives a double standard: life as a pilgrim, and life as a rich man. Whether the townsmen ever question this dichotomy is unknown to the reader. That is a sign of ambiguity.
Finally, the manner in which Dimmesdale dies and the town re-tells his story shows that it is also unknown to the reader whether the townsmen believed Dimmesdale's confession or if, instead, they chose to believe what they wanted. Even Hawthorne says
"The reader may choose among these theories."
Therefore, as a major theme, ambiguity plays the role of making the reader come to conclusions as far as the backbone of each character, about their actual state of mind, and about the mindset of the villagers as a community.