What allusions does Hawthorne make in The Scarlet Letter?

Because Hawthorne used so many allusions in the novel, the only way not to miss any is to read a well-footnoted edition such as the Norton Critical Edition. I will give you two examples from chapter one to get you started.
The second paragraph in the novel alludes to Sir Thomas Moore's 1515 Utopia, a fictional work with which both the colonists Hawthorne writes about and his readers in the nineteenth century would have been very familiar. Moore mean to contrast English or European society with what an ideal society would be like. Hawthorne's narrator points out the irony that a theocratic colony, a Utopia (ideal society), has decided one of its first buildings should be a prison. 
Another allusion—this one in the chapter's final paragraph—is a reference to Anne Hutchinson. Hawthorne's narrator speculates that the rose bush that grows beside the prison door "sprung up under [her] footsteps" as she entered the prison. Anne Hutchinson, like the fictional Hester Prynne, dared to defy the belief system of the paternalistic Puritan elders.