To compute an accurate K correction, one needs an accurate description of the source flux density f(), the standard-source flux densities gR() and gQ(), and the bandpass functions R() and Q(). In most real astronomical situations, none of these is known to better than a few percent, often much worse. Sometimes, use of the AB system seems reassuring (relative to, say, a Vega-relative system) because gAB() is known (i.e., defined), but this is a false sense: In fact the standard stars have been put on the AB system to the best available accuracy. This involves absolute spectrophotometry of at least some standard stars, but this absolute flux information is rarely known to better than a few percent. The expected deviations of the magnitudes given to the standard stars from a true AB system are equivalent to uncertainties in gAB().
The classical K correction has Q() = R() and gQ() = gR(). This eliminates the integrals over the standard-source flux density gR(). However, it requires good knowledge of the source flux density f() if the redshift is significant. Many modern surveys try to get R() ~ Q([1 + z]) so as to weaken dependence on f(), which can be complicated or unknown. This requires good knowledge of the absolute flux densities of the standard sources if the redshift is significant. This kind of absolute calibration is often uncertain at the few-percent level or worse.
Note that if equation (2) is taken to be the definition of the K correction, then the statement by oke68a that the K correction "would disappear if intensity measurements of redshifted galaxies were made with a detector whose spectral acceptance band was shifted by 1 + z at all wavelengths" becomes incorrect; the correct statement is that the K correction would not depend on the source's spectrum f().
It is a pleasure to thank Bev Oke for useful discussions. This research made use of the NASA Astrophysics Data System, and was partially supported by funding from NASA and NSF.