Open problems are clearly defined problems1 that have not been solved. In older fields, such as Mathematics, the list is rather intimidating. Rationality, on the other, seems to have no list.
While we have all of us here together to crunch on problems, let's shoot higher than trying to think of solutions and then finding problems that match the solution. What things are unsolved questions? Is it reasonable to assume those questions have concrete, absolute answers?
The catch is that these problems cannot be inherently fuzzy problems. "How do I become less wrong?" is not a problem that can be clearly defined. As such, it does not have a concrete, absolute answer. Does Rationality have a set of problems that can be clearly defined? If not, how do we work toward getting our problems clearly defined?
See also: Open problems at LW:Wiki
1: "Clearly defined" essentially means a formal, unambiguous definition. "Solving" such a problem would constitute a formal proof.
There's a difficulty here involving the fact that every finite set of possible counterexamples has measure zero in the set {(a, b, c, n) | a, b, c, n in N} equipped with the probability measure that assigns each possible counterexample an equal probability.
So all the usual biases and cognitive gotchas involving probability and infinity come into play (even when the people doing the thinking are mathematicians!), and all bets are off.
My hypothesis is that the commonly used prior for counterexample distributions is exponential. As the lower bound K >= a, b, c, n on possible counterexamples increases, the exponential is updated into something close to uniform on the rest of {(a, b, c, n) | a, b, c, n in N}.
This does somewhat dodge the question, but it does make a difference that an infinite set of counterexamples can be associated with each counterexample. That is, if (a,b,c,n) is not a solution to the Fermat equation, then (ka,kb,kc,n) isn't either for any positive integer k.