There might be several different categories of problems, from the literal "unsolved" (i.e. mathematics / physics) to systemic (i.e. human resources / advertising).
Some examples that come to mind:
Brand Influencer — "The Algorithm" prevents exposure, sales, etc.
Customer Service — Explaining warranty status, other than "because it's the least we have to do legally".
Mathematician — The length of pi is continually increasing, and there doesn't appear to be an end.
Software Engineering — Thoroughly understanding a codebase in a reasonable amount of time.
Ideally, this would be less of a "here's why X field is bad" thought exercise, and more of a "that's interesting, I wonder if X problem could be solved" thought exercise.
Some examples that come to mind:
Ideally, this would be less of a "here's why X field is bad" thought exercise, and more of a "that's interesting, I wonder if X problem could be solved" thought exercise.