What are the difficulties inherent in estimating compensating wage differentials empirically?

One problem that researchers face in attempting to estimate a compensating wage differential is that the data must be sufficiently rich in details both about workers and job characteristics in order to properly hold other things equal.  Such datasets are notoriously hard to come by.  A second problem that confounds estimation of compensating wage differentials is that some job characteristics, while ostensibly disagreeable, are not viewed as disagreeable by everyone.  For example, physically demanding work may be regarded by some as appealing rather than unpleasant and as a result we wouldn't observe a compensating differential for such work.