This paper contains an important message regarding the numerical modeling of left-handed media (LHM) using the finite-difference time-domain (FDTD) method which remains at the moment one of the main techniques used in studies of these exotic materials. It is shown that conventional implementation of the dispersive FDTD method leads to an inaccurate description of evanescent waves in the LHM. This defect can be corrected using spatial averaging at the interfaces. However, a number of results obtained using the conventional FDTD method have to be reconsidered. For instance, accurate simulation of subwavelength imaging by the finite-sized slabs of left-handed media does not reveal the cavity effect reported by Chen [Phys. Rev. Lett. 92, 107404 (2004)]. Hence the finite transverse dimension of LHM slabs does not have significant effects on the subwavelength image quality, contrary to previous assertions.