  We present results of long-slit spectroscopy in several positions of the
Orion nebula. Our goal is to study the spatial distribution of a large number
of nebular quantities, including line fluxes, physical conditions and ionic
abundances at a spatial resolution of about 1". We find that protoplanetary
disks (proplyds) show prominent spikes of T([N II]) probably produced by
collisional deexcitation due to the high electron densities found in these
objects. Herbig-Haro objects show also relatively high T([N II]) but probably
produced by local heating due to shocks. We also find that the spatial
distribution of pure recombination O II and [O III] lines is fairly similar, in
contrast to that observed in planetary nebulae. The abundance discrepancy
factor (ADF) of O^{++} remains rather constant along the slit positions, except
in some particular small areas of the nebula where this quantity reaches
somewhat higher values, in particular at the location of the most conspicuous
Herbig-Haro objects: HH 202, HH 203, and HH 204. There is also an apparent
slight increase of the ADF in the inner 40" around theta^1 Ori C. We find a
negative radial gradient of T([O III]) and T([N II]) in the nebula based on the
projected distance from theta^1 Ori C. We explore the behavior of the ADF of
O^{++} with respect to other nebular quantities, finding that it seems to
increase very slightly with the electron temperature. Finally, we estimate the
value of the mean-square electron temperature fluctuation, the so-called t^2
parameter. Our results indicate that the hypothetical thermal inhomogeneities
--if they exist-- should be smaller than our spatial resolution element.
