  We have obtained a deep 8-field XMM-Newton mosaic of M33 covering the galaxy
out to the D$_{25}$ isophote and beyond to a limiting 0.2--4.5 keV unabsorbed
flux of 5$\times$10$^{-16}$ erg cm$^{-2}$ s$^{-1}$ (L${>}$4$\times$10$^{34}$
erg s$^{-1}$ at the distance of M33). These data allow complete coverage of the
galaxy with high sensitivity to soft sources such as diffuse hot gas and
supernova remnants. Here we describe the methods we used to identify and
characterize 1296 point sources in the 8 fields. We compare our resulting
source catalog to the literature, note variable sources, construct hardness
ratios, classify soft sources, analyze the source density profile, and measure
the X-ray luminosity function. As a result of the large effective area of
XMM-Newton below 1 keV, the survey contains many new soft X-ray sources. The
radial source density profile and X-ray luminosity function for the sources
suggests that only $\sim$15% of the 391 bright sources with
L${>}$3.6$\times$10$^{35}$ erg s$^{-1}$ are likely to be associated with M33,
and more than a third of these are known supernova remnants. The log(N)--log(S)
distribution, when corrected for background contamination, is a relatively flat
power-law with a differential index of 1.5, which suggests many of the other
M33 sources may be high-mass X-ray binaries. Finally, we note the discovery of
an interesting new transient X-ray source, which we are unable to classify.
