We present the results of long-slit spectroscopy, in several positions, of the Orion Nebula. Our goal is to study the spatial distributions of a large number of nebular quantities, including line fluxes, physical conditions, and ionic abundances, at a spatial resolution of about 1". In particular, we have compared the O++ abundance determined from collisionally excited and recombination lines in 671 individual one-dimensional spectra covering different morphological zones of the nebula. We find that protoplanetary disks (proplyds) show prominent spikes of Te([N II), which is probably produced by collisional deexcitation due to the high electron densities found in these objects. Herbig-Haro objects show also relatively high values of Te([N II), but these are probably produced by local heating due to shocks. We also find that the spatial distribution of the pure recombination O II and [O III] lines is fairly similar. The abundance discrepancy factor (ADF) of O++ remains rather constant along the slit positions, except in some particular small areas of the nebula, such as at the locations of the most conspicuous Herbig-Haro objects. There is also an apparent slight increase of the ADF in the inner 40" around θ1 Ori C. We find a negative radial gradient of Te([O III) and Te([N II) in the nebula, based on the projected distance from θ1 Ori C. In addition, the ADF of O++ seems to increase very slightly with the electron temperature. Finally, we estimate the value of the mean-square electron temperature fluctuation, the so-called t2 parameter. Our results indicate that the hypothetical thermal inhomogeneities, if they exist, should be smaller than our spatial resolution element. Based on observations made with the 4.2 m William Herschel Telescope (WHT), operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.