Ab initio electronic structure methods have reached a satisfactory accuracy for the calculation of static properties, but remain too expensive for quantum dynamical calculations. Recently, an efficient semiclassical method was proposed to evaluate the accuracy of quantum dynamics on an approximate potential without having to perform the expensive quantum dynamics on the accurate potential. Here, this method is applied for the first time to evaluate the accuracy of quantum dynamics on an approximate analytical or interpolated potential in comparison to the quantum dynamics on an accurate potential obtained by an ab initio electronic structure method. Specifically, the vibrational dynamics of H2 on a Morse potential is compared with that on the full CI potential, and the photodissociation dynamics of CO2 on a LEPS potential with that on the excited 1^Pi surface computed at the EOM-CCSD/aug-cc-pVDZ level of theory. Finally, the effect of discretization of a potential energy surface on the quantum dynamics is evaluated.