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.
Huh? How is this an unsolved problem? It's known that pi is an irrational number, so it doesn't have an "end". We can always compute more digits. Or did you mean something different?