Using an electron transport model, we calculate the electron density of the electron impact-produced nighttime ionosphere of Mars and its spatial structure. As input we use Mars Global Surveyor electron measurements, including an interval when accelerated electrons were observed. Our calculations show that regions of enhanced ionization are localized and occur near magnetic cusps. Horizontal gradients in the calculated ionospheric electron density on the night side of Mars can exceed 10$^4$ cm$^-3$ over a distance of a few tens of km; the largest gradients produced by the model are over 600 cm$^-3$ km$^-1$. Such large gradients in the plasma density have several important consequences. These large pressure gradients will lead to localized plasma transport perpendicular to the ambient magnetic field which will generate horizontal currents and electric fields. We calculate the magnitude of these currents to be up to 10 nA/m$^2$. Additionally, transport of ionospheric plasma by neutral winds, which vary in strength and direction as a function of local time and season, can generate large (up to 1000 nA/m$^2$) and spatially structured horizontal currents where the ions are collisionally coupled to the neutral atmosphere while electrons are not. These currents may contribute to localized Joule heating. In addition, closure of the horizontal currents and electric fields may require the presence of vertical, field-aligned currents and fields which may play a role in high altitude acceleration processes.