The efficiency of replication error repair is a critical factor governing the emergence of mutations. However, it has so far been impossible to study this efficiency at the level of individual cells and to investigate if it varies within isogenic cell populations. In addition, why some errors escape repair remains unknown. Here we apply a combination of fluorescent labelling of the Escherichia coli Mismatch Repair (MMR) complex, microfluidics, and time-lapse microscopy, to monitor in real-time the fate of >20000 replication errors. We show that i) many mutations result from errors that are detected by MMR but inefficiently repaired ii) this limited repair efficiency is due to a temporal constraint imposed by the transient nature of the DNA strand discrimination signal, a constraint that is likely conserved across organisms, and iii) repair capacity varies from cell to cell, resulting in a subpopulation of cells with higher mutation rate. Such variations could influence the fitness and adaptability of populations, accelerating for instance the emergence of antibiotic resistance.