I agree that it may be unrealistic to expect fully functioning products out of a three day hackathon, but I am continually impressed by the amount that people accomplish in such a short period of time. Extreme time constraints can often be a useful tool to break conventional thinking and prompt disruptive solutions.

Here's two suggestions that might produce a more focused outcome and reduce wasted effort:

1) Engage key stakeholders throughout the hackathon - so that a deeper understanding of their problems is reflected in the hacked solutions

2) Offer an "overtime" session for those who are interested in working with the stakeholder over an extended period (a few weeks or possibly months) to refine the solution