Understand what the interviewer is really getting at, so you can best tailor your response. What they really want to know is how you approach challenges, what you learned from the experience, and how you constructively applied that knowledge to other situations. In addition to gleaning a sense of your weaknesses, they’re trying to assess your problem-solving skills and potential for growth. (They also want to see if you’re honest.)

Most of us have had to face the dreaded, “Tell me about a time you made a mistake” question while interviewing for a new job.

And while the whole point of an interview is to put your best foot forward—and nobody relishes disclosing past work failures—with a little advanced prepara...