How about law? Obviously there are non-technical problems there as well, but it seems like there is still a lot that could be done technologically to improve transparency and (maybe more interestingly) reduce expense.
In the past one would gather a room full of lawyers and actually read through all of the documents (a task I did once). Now you can use a combination of linguists, lawyers, and search techniques to do the job.
(the discovery phase of a trial on average accounts for 50% of litigation expenses)