Radio-frequency (RF) photoinjector-based relativistic ultrafast electron diffraction (UED) is a promising new technique that has the potential to probe structural changes at the atomic scale with sub-100 fs temporal resolution in a single shot. We analyze the limitations on the temporal and spatial resolution of this technique considering the operating parameters of a standard 1.6 cell RF gun (which is the RF photoinjector used for the first experimental tests of relativistic UED at Stanford Linear Accelerator Center; University of California, Los Angeles; Brookhaven National Laboratory), and study the possibility of employing novel RF structures to circumvent some of these limits.