What aspects of the story thus far make you wonder whether the results of the experiment are real or not?

Hawthorne almost immediately invites the reader to call the entire story into question with the following line:

...Doctor Heidegger was a very strange old gentleman, whose eccentricity had become the nucleus for a thousand fantastic stories. Some of these fables, to my shame be it spoken, might possibly be traced back to mine own veracious self; and if any passages of the present tale should startle the reader's faith, I must be content to bear...

Hawthorne almost immediately invites the reader to call the entire story into question with the following line:

...Doctor Heidegger was a very strange old gentleman, whose eccentricity had become the nucleus for a thousand fantastic stories. Some of these fables, to my shame be it spoken, might possibly be traced back to mine own veracious self; and if any passages of the present tale should startle the reader's faith, I must be content to bear the stigma of a fiction-monger.

So he acknowledges that Doctor Heidegger was a strange man, which resulted in a lot of stories being told about him. He immediately raises the question of whether the tale that follows is not one of these stories and the narrator a "fiction-monger." The story is, of course, full of fantastic occurrences: first a rose, then a group of elderly people, then a butterfly brought back to youth with an elixir drawn from the legendary Fountain of Youth in Florida and shipped to the doctor by a friend. His elderly guests return to their youthful selves, at turns coquettish, politically inspired, and concocting far-fetched schemes to get ice to the tropics by harnessing whales to icebergs. As they flirt and act with youthful abandon, further doubt is cast on the "experiment" when the narrator notes that a mirror in the room "is said to have reflected the figures of the three old, gray, withered grand-sires, ridiculously contending for the skinny ugliness of a shrivelled grandam." In other words, their appearances do not seem to have actually changed. After the effects of the elixir (which has spilled) wear off, they are left to ask themselves whether it was all an illusion. But they all agree (except Dr. Heidegger) to go to Florida in search of the Fountain of Youth. So throughout the story, Hawthorne raises doubts about the extent, or even the existence, of the transformation of the elderly foursome.