  We present a new method for detecting and correcting systematic errors in the
distances to stars when both proper motions and line-of-sight velocities are
available. The method, which is applicable for samples of 200 or more stars
that have a significant extension on the sky, exploits correlations between the
measured U, V and W velocity components that are introduced by distance errors.
We deliver a formalism to describe and interpret the specific imprints of
distance errors including spurious velocity correlations and shifts of mean
motion in a sample. We take into account correlations introduced by measurement
errors, Galactic rotation and changes in the orientation of the velocity
ellipsoid with position in the Galaxy. Tests on pseudodata show that the method
is more robust and sensitive than traditional approaches to this problem. We
investigate approaches to characterising the probability distribution of
distance errors, in addition to the mean distance error, which is the main
theme of the paper. Stars with the most overestimated distances bias our
estimate of the overall distance scale, leading to the corrected distances
being slightly too small. We give a formula that can be used to correct for
this effect. We apply the method to samples of stars from the SEGUE survey,
exploring optimal gravity cuts, sample contamination, and correcting the used
distance relations.
