Between two of the bookcases hung a looking-glass, presenting its high and dusty plate within a tarnished gilt frame. Among many wonderful stories related of this mirror, it was fabled that the spirits of all the doctor's deceased patients dwelt within its verge, and would stare him in the face whenever he looked thitherward. (3)
Again, this is rather creepy. The mirror, like the black folio and the skeleton in the closet, complicates Dr. Heidegger's character and adds yet another sinister shadow to a growing collection of dark secrets. If Dr. Heidegger has that many dead patients, we might wonder if he's a very good doctor at all. Is he haunted by their spirits? If so, is it because he is guilty for their deaths? Or does he simply feel guilty because he's a good man, yet bears no actual responsibility? Or perhaps he is not haunted by these spirits, but as with Hippocrates, consults with and can learn from them. We really can't be sure. Add this to the list of quasi-supernatural Heidegger riddles we can't quite crack.
You've also got the mirror playing an interesting role later in the text. As Heidegger's four guests romp about the study, "never was there a livelier picture of youthful rivalship, with bewitching beauty for the prize" (41). The narrator goes continues:
Yet, by a strange deception, owing to the duskiness of the chamber, and the antique dresses which they still wore, the tall mirror is said to have reflected the figures of the three old, gray, withered grandsires, ridiculously contending for the skinny ugliness of a shriveled grandma. (41)
First of all, there's quite a bit of narrative trickery here in the phrase "is said to." The mirror is said to have reflected the guests as old. Said by whom? Who is telling this story, anyway? This makes it sound like the narrator heard the tale from someone else, despite having earlier insinuated that he is the source. Weird.
Also, we don't know what to make of the mirror's reflection. It might mean that the elixir is real, but only transforms its drinkers physically. The mirror, which has its own mystical powers, is able to reflect the real nature of the romping guests (in their souls, they are still old). Or, it could be that the mirror is perfectly ordinary, and the elixir is totally fake. The mirror shows us reality, whereas the guests are prancing about in an alcohol-induced stupor. One thing we can be sure of is that Hawthorne wants us asking these questions; the mirror is just another detail that keeps us guessing.