Particle tracking of active colloidal particles can be used to compute mean-squared displacements that are fit to extract properties of the particles including the propulsive speed. Statistical errors in the mean-squared displacement leads to errors in the extracted properties especially for more weakly propelling particles. Brownian dynamics simulations in which the particle parameters are prescribed were used to examine the statistics of tracking self-propelling objects. It was found that the manner in which tracking data is analyzed has a profound impact on the precision and accuracy of measurements. To properly extract particle parameters, it was necessary to apply a nonlinear fit of the mean-squared displacement over a time region that includes transition behavior from ballistic to diffusive. The dependence of the statistics on the number of particles tracked and the length of movies was examined, showing how and why weakly propelling particles are difficult to analyze.