I would be interested in developing a theory of saliency for scientific hypotheses. My current field, computer vision, has had some interesting results where saliency can be targeted for specific object types. For example, you could train a "people spotter" and a "bicycle spotter" and then go look at a scene. Both spotters will report false positives, etc., but the spotters give you some confidence (a) about whether the thing you want to find is even in the scene and (b) where in the scene to burn your resources when looking for it.

I'm not claiming it would be straightforward at all, but a conversion of this approach aimed at detecting salient ideas would seem to be the right direction. It raises some questions of immediate interest: what sort of feature vector should one extract to quantize an idea? There must be ways to describe a set of experiments, say, of maximum mutual information with respect to a set of hypotheses... that is, you can literally compute the experimental redundancy between a set of experiments and whittle them down to the ones that bear the maximal relevance w.r.t. some set of hypotheses.