What are some examples of allusions in The Scarlet Letter?

One of the earliest allusions in the novel is to Anne Hutchinson. Now, others have mentioned this, but, as is the case with most allusions, the important part is knowing who Anne Hutchinson was and what mentioning in relation to Hester is saying about our protagonist.

Anne Hutchinson was a real person, and, like our fictional Hester, defied Puritan law. Her crime was defying Puritan teachings both by subscribing to a different take on salvation and by teaching it to others. Puritans believed in predestination. They also placed a good deal of emphasis on works. In other words, in a sense, performing good acts is a means of ensuring salvation. Anne Hutchinson believed in "a covenant of grace." This was based on the preaching of a man by the name of John Cotton. The covenant of grace maintained that no amount of good works could "earn" a person a spot in heaven, but rather salvation was received via the grace of God. It was a gift given by Him and solely at his discretion.

In believing in the covenant of grace, Anne Hutchinson was rebelling against traditional, Puritan teachings. Hester Prynne also rebelled against Puritan teachings by committing adultery. Now, you may be thinking that disagreeing with church teachings is not the same as committing adultery, and to our more modern way of approaching spirituality, perhaps it isn't. But to the Puritans, a sin was a sin. No distinction was made based on what the sin was, how it was committed, etc. Anne Hutchinson (who again was a real person) had grown into a sympathetic character in the eyes of Hawthorne's audience whose views of spirituality were also quite different than those of the Puritans. In a sense, by alluding to Anne Hutchinson in regard to Hester, Hawthorne is seeking an extension of that sympathy toward his fictional character. It is as though he is saying, "Hey, you know this lady (Hutchinson) was treated badly, and now I am presenting you with a character who, in many ways, is also being treated badly."

You have likely done something similar in your real life. Think about approaching your parents about wanting a particular gift for Christmas. Have you ever, in asking for it, alluded to a past Christmas when your desired gift wasn't received? "Mom and Dad, I would sure like a new cell phone for Christmas. Remember a few years ago when I asked for that ten-speed bike and you weren't able to get it? Well, I understand now that money was tight and that wasn't possible, but with you (Dad) getting that new job, well, I was hoping I could get a new cell phone. I can pitch in..."

Hawthorne is employing a similar technique in alluding to Hutchinson. Whether or not it gains any sympathy for Hester is dependent on your knowledge of Anne Hutchinson. I suppose what I am trying to say is this. The allusions contained in The Scarlet Letter are plentiful, but the more important thing is what they mean or what they are saying. When you come across one, take a moment to look up the reference. If you do, you will not only enhance your reading experience, but you will find better and deeper material from which to write about, talk about and interact with the story.