The characters in "Dr. Heidegger's Experiment" are given a chance to go back and change mistakes they had made. If given the chance to go back in time and change something, are humans capable of doing so? If so, how unusual or difficult is it? Please be sure to give examples from real life.
You are correct in assuming that the characters in "Dr. Heidegger's Experiment" are given a chance to go back in time and change the mistakes that they have made. These characters are four elderly people: three men and one woman. The way they are given a chance is by taking a drink from the mysterious waters of the Fountain of Youth that Dr. Heidegger has procured and brought a withered rose back to life. Note their original reaction even before drinking:
The doctor's four venerable friends made him no answer, except by a feeble and tremulous laugh; so very ridiculous was the idea that, knowing how closely repentance treads behind the steps of error, they should ever go astray again.
Unfortunately, they become fairly intoxicated by the drink, lose their inhibitions, make fun of the doctor, and generally take on the immaturity of the young. As a result, in their rabble rousing, they knock over the special vase with the water from the Fountain of Youth and they all become old again. Therefore, they were "given a chance" but they didn't take it due to their own immaturity.
Now that we've explored how the characters of the story were able to be "given a chance," let's talk about your actual question as to whether the humans of today would be capable of that chance. I believe some humans would be capable while other humans would not, and I am happy to give examples.
Because the success of changing something in the past depends on the maturity of the younger person, those who would not be capable of doing so are those young adults who are quite immature. I'm afraid this would be most people. If you look at the quotation above, immaturity is apparent through the laughter, even of the elderly. Let me give a few examples that might make this seem real even in today's context. There are people in high school and college who haven't "found themselves." They drink until they pass out, they take risks with alcohol and drugs, they fail classes (or even refrain from going to them), they balk at responsibility, they talk back to their parents and sneak out at night. In short, they believe that they are indestructible and that death has no meaning from them. They have not yet learned the value of their own mortality. These are the kind of people who might squander the fountain of youth. They might return to their former selves and seek the intoxication of drunkenness or unprotected sex. As a result, they might endanger their lives and wouldn't be capable of making a change for the better. I would assert that this would describe most humans, unfortunately. We are all guilty of immaturity at some point in our lives. If we happened to relive that moment, our endeavor to change something important would be doomed to failure.
Then there are those people who, even as little babies, the parents often call "old souls." For repetition's sake, because the success of changing something in the past depends on the maturity of the younger person, those who WOULD be capable of doing so are young adults who are incredibly mature beyond their age. Sometimes these young people are forced into that maturity by something like losing a parent and having to cultivate other siblings, other times they are forced into that maturity by being part of a large family and having to parent themselves, still other times extreme intelligence from birth might be in the picture. There are also young people who are very intuitive and "just know" things from a very young age. I believe that, due to their intense maturity, these persons are capable enough at a young age to be able to make any changes they are determined to make.
Because this is a major philosophical question, I have to admit that there is also a MAJOR caveat here. Ironically, if that very mature young person originally made the mistake at that same age, there is no way they would know enough to change it when they reverted to that age. Therefore, even those of great maturity would have to correct SOMEONE ELSE'S mistake because they would not be able to correct their own (that they made at that same immaturity level), ... UNLESS they were able to somehow know what happened in the future as a result and depend on their intelligence to remember. However, there is no indication in "Dr. Heidegger's Experiment" that the memory of the future exists. (Then again, the four people he chose were quite immature as young adults.)
The first bit of grand irony is that Dr. Heidegger HIMSELF just might have been mature enough as a young man to handle that big of a change. Note what he says here:
For my own part, having had much trouble in growing old, I am in no hurry to grow young again.
Why is this significant? Because Dr. Heidegger admits that he DID have those very "troubles" that cause a young person to mature quite fast. Perhaps HE would have been able to achieve the changes you suggest!
The other irony of your question is that there is NO WAY to give actual "examples from real life" because no one has ever found the Fountain of Youth; therefore, no one has ever been able to take that chance. Still, this entire thought process reminds me intensely of Jonathan Swift's description of the Skuldruggs in his Gulliver's Travels. Born with a strange mark on their heads, these humans were destined to live forever. Instead of being a mark of joy, it is a mark of despair. The people live for the usual amount of time normally, but it isn't long before all those they know and love die and then they lose all teeth and hair and abilities. They eventually long for death. The moral of your question is this: be careful what you wish for, because you just might get it!
Your question reminded me of a novel I read many years ago: Strange Life of Ivan Osokin by P. D. Ouspensky, a Russian mystic with some really far-out ideas. According to the coverage in Wikipedia:
Strange Life of Ivan Osokin (Russian: Странная жизнь Ивана Осокина) is a novel by P. D. Ouspensky. It follows the unsuccessful struggle of Ivan Osokin to correct his mistakes when given a chance to relive his past.
The book was published in Russian in 1915 but not in English until 1947. The hero Ivan Osokin is given a chance to live his life all over again. He finds that he is helpless to change a single thing and has to live exactly the same life he lived before. Reliving his youth is not an enjoyable experience, as I remember, but a sort of drudgery. It is something like watching a dull motion picture over again, when you didn't like it very much the first time you sat through it. We can all have this experience today because some TV channels will show the same old movie over and over for a full week.
Ouspensky lived from 1878 to 1947. His best-known works are In Search of the Miraculous and Tertium Organum. It seems possible that he might have gotten his idea for Strange Life of Ivan Osokin from Nathaniel Hawthorne's story "Dr. Heidegger's Experiment."