By making this information easily accessible we lower the barriers to people to find a problem to solve, giving them a rewarding challenge, and most importantly, getting problems solved.
How to create and structure this dataset? The is an obvious one for input from the crowd. Probably the closest example would be Wikipedia, with a vast number of content creators, and a smaller number of content curators. Each problem entry would have: a title; a description; an estimate of the number of people affected; an estimate of the social/environment/economic (triple-bottom-line) cost; an estimate of the extent that the problem/need is being addressed by current technologies, techniques, policies, etc (this is important as problems/needs that we consider 90% solved should still be on the database as that 10% is important); links to other problems; links to parent/daughter problems (a interlinked hierarchical dataset is appropriate); solution discussion (potentially a forum per problem).
Users of the tool can add content, suggest solutions, vote on what problems are most pressing, etc.
Startup companies can reference the problem/need tool, explaining what problem they're solving, or what need they're addressing, providing evidence to the would-be investors of the necessity for (and indicative benefit of) their investment.
Pure science researchers can more easily find applications of their blue skies research.