In Stave 1, the narrator makes an allusion to Shakespeare's Hamlet. In this play, the father of young prince Hamlet dies only to reappear to him as a ghost that demands revenge for his death. The narrator of A Christmas Carol claims that viewers of Hamlet must be convinced of King Hamlet's death if they are to find his appearance by the tower remarkable:
If we were not perfectly convinced that Hamlet's Father died before the play began, there would be nothing more remarkable in his taking a stroll at night, in an easterly wind, upon his own ramparts, than there would be in any other middle-aged gentleman rashly turning out after dark in a breezy spot.
On the most basic level, this allusion introduces the theme of ghosts, continues the motif of death from the first page, acknowledges Dickens's greatest literary forefather, and foreshadows Marley's return as a ghost. On a deeper level, though, it encourages readers to compare and contrast Hamlet and A Christmas Carol. The titular character goes mad and dies at the end of the play, whereas Scrooge gets a happy ending. This allusion hints that the story could potentially be a tragedy—but it is not.
All the ghosts implicitly demand that Scrooge change his ways. The ghosts are therefore advocates of justice in both Hamlet and A Christmas Carol. They derive authority from their otherworldly appearances; living characters take heed of their advice because they are in awe. The allusion is also intended to have a comedic effect—it is used to humorously reinforce what Dickens says in the very first paragraph, which establishes that Marley is "dead as a door-nail."
Marley's ghost makes an apt allusion to the Star of Bethlehem, which guided the Wise Men to Jesus shortly after he was born. In this passage, Marley's ghost recalls being an ignorant man who ignored the plights of other people:
"Why did I walk through crowds of fellow-beings with my eyes turned down, and never raise them to that blessed Star which led the Wise Men to a poor abode? Were there no poor homes to which its light would have conducted me!"
This biblical allusion reflects the fact that Marley's speech resembles Christian repentance. He regrets being so stingy and understands that his heavy chains are a punishment for having poor character throughout his life. This allusion shows what Marley could have been—a wise and generous man who brings gifts and joy to other people's lives.
Scrooge still has a chance to change his ways and raise his eyes to the star, so to speak, in order to help others and escape Marley's fate. The whole point of Marley's appearance is to scare Scrooge into believing that he will suffer similar consequences if he does not change his ways. The Wise Men brought gifts to Jesus by the light of this star; Scrooge bring gifts to his community through the wisdom of the spirits. In other words, Scrooge remains lost in the darkness of greed and misery until the spirits show him the grave consequences of his actions.