Consider how the text presents his former beloved and what it says about her fate:
The opposite side of the chamber was ornamented with the full-length portrait of a young lady, arrayed in the faded magnificence of silk, satin, and brocade, and with a visage as faded as her dress. Above half a century ago, Dr. Heidegger has been on the point of marriage with this young lady; but, being affected with some slight disorder, she had swallowed one of her lover's prescriptions and died on the bridal evening.
This quote therefore provides us with crucial information regarding Dr. Heidegger as a character. He is clearly a tragic figure, living with the guilt of having killed the one he loved, perhaps not through his own fault, but clearly feeling some kind of responsibility. I don't necessarily think that this quote suggests Dr. Heidegger is incompetent, but it definitely does present us with an incredibly tragic man - how would you live with yourself if on your advice your lover had taken a medicine which ended up killing them? It presents us with a thoughtful, sombre and reflective character who has been driven to explore ways to conquer death and time, but who, following his experiment, is able to recognise the benefits of age.