We introduce a procedure based on Wadati diagrams to assess and improve the consistency of P- and S-wave travel-time picks with the assumption of propagation at constant wave-speed. Wadati diagrams are plots of S-P vs P-wave travel-times and they are expected to lie along a straight line for a medium of constant velocity. Our procedure automatically searches for the largest subset of (P,S-P) travel-time pairs with regression coefficient above 0.9, which effectively removes travel-times associated with non-homogeneous ray-paths. Inaccuracies in travel-time picks due to clock drifts or complex arrivals and/or erroneous event associations are also identified and eliminated through this procedure. An application to P- and S-wave travel-times from 11,224 events recorded during 2007 on an in-mine network in Savuka mine near Carletonville (South Africa), reveals that a high correlation coefficient alone is not sufficient to ensure consistency. The histogram of vp/vs values inferred from the slopes of the Wadati diagrams peaks at values of 1.62 to 1.63, in agreement with the underlying geology, but a significant portion of the catalogued events show unrealistic vp/vs values. Adding realistic constraints on the slopes of the linear fits to the Wadati filter is critical to ensure the consistency of the travel-time picks. Event relocations obtained for the filtered data set assuming propagation at constant wave-speed do not deviate significantly from locations reported by the in-mine network operator.