For a class of problems, a combination of algorithms and human input makes for the most optimal solution. For instance, three years ago software to recreate shredded documents that won the DARPA award used “human[s] [to] verify what the computer was recommending.” The insight is used in character recognition tasks. I have used it to create software for matching dirty data — the software was used to merge shape files with electoral returns at precinct level.
The class of problems for which human input proves useful has one essential attribute — humans produce unbiased, if error-prone, estimates for these problems. So for instance, it would be unwise to use humans for making the ‘last mile’ of lending decisions (see also this NYT article). (And that is something you may want to verify with training data.)