We conduct a comprehensive investigation into the electronic and magnetotransport properties of ZnO nanoplates grown concurrently with ZnO nanowires by the vapor-liquid-solid method. We present magnetoresistance data showing weak localization in our nanoplates and probe its dependence on temperature and carrier concentration. We measure phase coherence lengths of 50--100 nm at 1.9 K and, because we do not observe spin-orbit scattering through antilocalization, suggest that ZnO nanostructures may be promising for further spintronic study. We then proceed to study the effect of weak localization on electron mobility using four-terminal van der Pauw resistivity and Hall measurements versus temperature and carrier concentration. We report an electron mobility of $\ensuremath{\sim}100\text{ }{\text{cm}}^{2}/\text{V}\text{ }\text{s}$ at 275 K, comparable to what is observed in ZnO thin films. We compare Hall mobility to field-effect mobility, which is more commonly reported in studies on ZnO nanowires and find that field-effect mobility tends to overestimate Hall mobility by a factor of 2 in our devices. Finally, we comment on temperature-dependent hysteresis observed during transconductance measurements and its relationship to mobile, positively charged Zn interstitial impurities.