After Baglioni warns Giovanni about Rappaccini’s immorality and his professional stature as a scientist, the narrator uses dramatic irony to foreshadow Baglioni's cruel machinations at the end of the story:
[Giovanni] might have taken Baglioni's opinions with many grains of allowance had he known that there was a professional warfare of long continuance between him and Dr. Rappaccini, in which the latter was generally thought to have gained the advantage. If the reader be inclined to judge for himself, we refer him to certain black-letter tracts on both sides.
Here, the narrator gives the reader a key piece of information that Giovanni lacks—namely, that Baglioni’s condemnation of Rappaccini is rooted in jealousy. As a result, his assessment of Rappaccini is likely to be biased. In the hopes of bringing down his professional rival, Baglioni has a motive to harm Beatrice, and Giovanni is completely unaware of this dynamic. As a result, the dramatic irony here leads the reader to suspect that Baglioni is plotting something—and that Giovanni will fail to anticipate it. Moreover, the narrator’s observation that Giovanni “might have” acted differently had he been given this information reveals to the reader that he will make a fatal error due to his ignorance. This heightens the ominous mood of the story and foreshadows its tragic ending.
In "Rappaccini's Daughter," the character Beatrice’s name is an allusion to the Divine Comedy, a long narrative poem by the Italian poet Dante Alighieri that follows the poet himself as he journeys through hell, purgatory, and paradise. This allusion in "Rappaccini's Daughter" adds some insight into both Giovanni's and the reader's initial uncertainty about whether Beatrice is good or evil. In the Divine Comedy, Beatrice serves as Dante's deceased love interest and guide in the final part of the Purgatorio as well as the Paradiso. In Inferno, she's the one who sends the famous ancient poet Virgil to guide Dante through hell, wanting to make sure he's protected on this leg of the journey so that he can eventually join her in heaven. She is, then, presented as the pinnacle of moral purity, grace, and femininity.
Beatrice's name initially seems ironic, given our suspicions that she is complicit in the unknown evils of Rappaccini's garden. And yet, the more we see of Beatrice, the more fitting her virtuous namesake comes to seem: she even crosses herself over the death of an insect. In this way, Beatrice's name suggests her moral purity even before the story confirms that she is not intentionally poisoning Giovanni. Ultimately, Beatrice's name, with its allusion to Dante's heavenly guide, emphasizes the irony that Giovanni could deceive himself about someone who is so obviously good rather than evil.