One problem that springs to mind is the origin of life. There's mountains of evidence relating to this topic - and I expect a rational agent could figure out many of the important details if given the existing public evidence. I expect LessWrong would do badly on this topic - due to lack of knowledge.

Another topic is how - in practice - to implement an oracle - a.k.a. a resource-limited Solomonov induction agent. That plays to LessWrong strengths - and is based on a "neat" pure maths problem.