  Spectra of nearly 20000 point-like objects to a Galactic reddening corrected
magnitude of i=19.1 have been obtained to test the completeness of the SDSS
quasar survey. The spatially-unresolved objects were selected from all regions
of color space, sparsely sampled from within a 278 sq. deg. area of sky covered
by this study. Only ten quasars were identified that were not targeted as
candidates by the SDSS quasar survey (including both color and radio source
selection). The inferred density of unresolved quasars on the sky that are
missed by the SDSS algorithm is 0.44 per sq. deg, compared to 8.28 per sq. deg.
for the selected quasar density, giving a completeness of 94.9(+2.6,-3.8) to
the limiting magnitude. Omitting radio selection reduces the color-only
selection completeness by about 1%. Of the ten newly identified quasars, three
have detected broad absorption line systems, six are significantly redder than
other quasars at the same redshift, and four have redshifts between 2.7 and 3.0
(the redshift range where the SDSS colors of quasars intersect the stellar
locus). The fraction of quasars missed due to image defects and blends is
approximately 4%, but this number varies by a few percent with magnitude.
Quasars with extended images comprise about 6% of the SDSS sample, and the
completeness of the selection algorithm for extended quasars is approximately
81%, based on the SDSS galaxy survey. The combined end-to-end completeness for
the SDSS quasar survey is approximately 89%. The total corrected density of
quasars on the sky to i=19.1 is estimated to be 10.2 per sq. deg.
