In this paper, we show the potential of webcams as precision measuring instruments in a physics laboratory. Various sources of error appearing in 2D coordinate measurements using low-cost commercial webcams are discussed, quantifying their impact on accuracy and precision, and simple procedures to control these sources of error are presented. Finally, an experiment with controlled movement is performed to experimentally measure the errors described above and to assess the effectiveness of the proposed corrective measures. It will be shown that when these aspects are considered, it is possible to obtain errors lower than 0.1%. This level of accuracy demonstrates that webcams should be considered as very precise and accurate measuring instruments at a remarkably low cost. (Contains 8 figures.)