  The dynamic capture of electrons in a semiconductor quantum dot (QD) by
raising a potential barrier is a crucial stage in metrological quantized charge
pumping. In this work, we use a quantum point contact (QPC) charge sensor to
study errors in the electron capture process of a QD formed in a GaAs
heterostructure. Using a two-step measurement protocol to compensate for $1/f$
noise in the QPC current, and repeating the protocol more than $10^{6}$ times,
we are able to resolve errors with probabilities of order $10^{-6}$. For the
studied sample, one-electron capture is affected by errors in $\sim30$ out of
every million cycles, while two-electron capture was performed more than $10^6$
times with only one error. For errors in one-electron capture, we detect both
failure to capture an electron, and capture of two electrons. Electron counting
measurements are a valuable tool for investigating non-equilibrium charge
capture dynamics, and necessary for validating the metrological accuracy of
semiconductor electron pumps.
