Some high-profile interesting questions in the recent past:
- If you're a theoryCS conference organizer/PC chair, or plan to be one in the near future, you should really read "Small steps for better TCS conferences?", asked by Jukka Suomela. There are fantastic suggestions for small things (i.e low to zero expense) that can be done to make theoryCS conferences better in many ways.
- Ashley Montanaro asks if there are any efficient algorithms for counting problems that don't go through a determinant calculation.
- Don Sheehy wonders whether the $d^d$ term in deterministic $\epsilon$-net constructions is necessary.
- Vinayak Pathak asks about "non-geometric" problems whose solutions involve some critical geometric insight. Ken Clarkson provides a number of good examples, and Sariel Har-Peled gets bonus points for citing Monty Python.