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Although photometric redshifts (photo-z’s) are crucial ingredients for current and upcoming large-scale surveys, the high-quality spectroscopic redshifts currently available to train, validate, and test them are substantially non-representative in both magnitude and colour. We investigate the nature and structure of this bias by tracking how objects from a heterogeneous training sample contribute to photo-z predictions as a function of magnitude and colour, and illustrate that the underlying redshift distribution at fixed colour can evolve strongly as a function of magnitude. We then test the robustness of the galaxy–galaxy lensing signal in 120 deg2 of HSC–SSP DR1 data to spectroscopic completeness and photo-z biases, and find that their impacts are sub-dominant to current statistical uncertainties. Our methodology provides a framework to investigate how spectroscopic incompleteness can impact photo-z-based weak lensing predictions in future surveys such as LSST and WFIRST.