Many seismological studies depend on the accuracy of timing of seismological data. In seismic tomography, travel-time residuals defined as differences between the observed and calculated arrival times of seismic phases are minimized to constrain 3D velocity structure. Inconsistencies and large errors in data sets that result from incorrect station coordinates, errors in the timing acquisition system, errors in the merging procedure, inconsistency in the picking and phase misidentification can also generate travel-time residuals, and because of their systematic nature, these errors cannot be treated as random noise even by exploiting a large number of travel times. While the inverse problem is perfectly set up to deal with random noise, systematic errors lead to significant artifacts in the solution, but may not be detected by a posterior error assessment. For this reason, detecting and removing systematic travel-time errors from data sets before inversion is crucial for seismic tomography studies.We present a methodology based on the use of a minimum 1D model to detect and remove systematic errors in travel-time data by detailed analysis of station delays and observation residuals and apply it to a local earthquake data set from Costa Rica. The determination of the exact nature of detected inconsistencies needs further investigations in each individual case. If the cause of detected systematic errors cannot be determined beyond any doubt and the afflicted data may not be corrected, they must be deleted from the data set. To assess the extent of influence of systematic errors on hypocenter locations and their uncertainties, we present two examples showing the effects of station mislocation.