Studies of historic earthquake ground surface ruptures show that displacements along strike are spatially variable. As a result, latest Quaternary slip rates developed from a spatially restricted set of cumulative displacement measurements may not accurately represent fault velocity. Here we examine the uncertainties associated with slip on the Cucamonga Fault, which is part of a network of faults that have generated damaging historical earthquakes in and around Los Angeles, California. Numerous scarps along its ~25‐km length are well expressed on alluvial fans. We make 310 measurements of vertical separation across the scarps using lidar data. We show that the dispersion of the vertical separations cannot be explained by our best estimates of analytical uncertainties alone. Additional epistemic uncertainties are required. We find that the magnitude of the required epistemic uncertainty is typically larger than analytical uncertainty by a factor of 3 and typically about 22% of the maximum vertical separation. These relationships appear to hold at several spatial scales. We examine three potential sources of epistemic uncertainty and find that none among surface age uncertainty, fault dip, and anthropogenic landscape alteration is likely sufficient to explain the overdispersion of the data, which suggests differences in cumulative strain along the strike of the fault. We calculate a range of dip‐slip rates between 0.4 and 2.6 mm/year. In light of our results, we suggest that future thrust‐fault slip‐rate studies adopt an epistemic uncertainty of 22% of the maximum value for vertical separation measurements, unless there are sufficient data to demonstrate otherwise.