[pav3l]

This is a very good question. I work at a large Canadian hospital in research environment. I see inefficiencies every day, tons of them, I'm seeing new startup opportunities every week.

For example there are lots of problems that could benefit from applications of Machine Learning and modern statistical learning theory, but people working on the problems don't have enough Math/CS background and not sure who to turn to; the quality of data analysis in Nursing/Psychiatry/Paliative care/etc areas is much inferior to, say, quality of data analysis people do in physics or finance; the widely used software (e.g. SPSS, Excel) is mostly crap and things could get done much faster and less error prone if appropriate technologies were developed. I could probably go on forever...