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 $Te([N ^{t{$ -->$t Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->, 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 $Te([N ^{t{$ -->$t Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->, 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 $Te([O ^{t{$ -->$t Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([O ^{t{$ -->$t Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([O ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([O ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([O ^{t{$ --> and $Te([N ^{t{$ -->$t Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ -->$t Igt tt/Igt Igt tt/Igt Igt tt/Igt Igt Tt/Igt t SUBgt t Igt et/Igt t/SUBgt ([N ^{t{$ --> 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.