The Scarlet Letter is very obviously a novel which speaks out about the general hypocrisy of the Puritan leaders, most notably the governors. Hawthorne shows this in nearly every scene in which Governor Bellingham is present.
After meeting this character in Chapter 2 at the first scaffold scene we see that he is an equal proponent of religion and law. He condemns Hester Prynne before the eyes of everyone, and when he cannot get a response from her, he defaults to the minister hoping his relationship with her (as a congregant) will help. Later, in Chapter 8, we see that the governor wishes to take Pearl away from her mother, suspecting Hester is not raising Pearl according to proper Puritan standards.
While acting as a "stern magistrate" over all things both legal and holy (for to him, these are one and the same) he himself is not living up to the standards he demands of his citizens. For example, he wishes the colonists to live simple and pious lives, not drawing attention to themselves with fancy clothes and houses. He lives in a highly decorated house and wears the most elaborately decorated clothes of anyone in town (made by Hester). In addition to the general attention he draws to himself by this alone, he also spends one day a year (Election Day) celebrating himself and his position.
In short, Governor Bellingham (representing the magistrates of the time in general) is willing to issue decrees, punishments, and advice about how to live a "pure" life, but he is unwilling to practice exactly what he preaches. This hypocrisy is one of the themes for which Hawthorne is most famous as a Romantic author.