  We examine the effect of point source confusion on cluster detection in
Sunyaev-Zel'dovich (SZ) surveys. A filter matched to the spatial and spectral
characteristics of the SZ signal optimally extracts clusters from the
astrophysical backgrounds. We calculate the expected confusion (point source
and primary cosmic microwave background [CMB]) noise through this filter and
quantify its effect on the detection threshold for both single and multiple
frequency surveys. Extrapolating current radio counts, we estimate that
confusion from sources below 100 microJy limits single-frequency surveys to
1-sigma detection thresholds of Y 3.10^{-6} arcmin^2 at 30 GHz and Y 10^{-5}
arcmin^2 at 15 GHz (for unresolved clusters in a 2 arcmin beam); these numbers
are highly uncertain, and an extrapolation with flatter counts leads to much
lower confusion limits. Bolometer surveys must contend with an important
population of infrared point sources. We find that a three-band matched filter
with 1 arcminute resolution (in each band) efficiently reduces confusion, but
does not eliminate it: residual point source and CMB fluctuations contribute
significantly the total filter noise. In this light, we find that a 3-band
filter with a low-frequency channel (e.g, 90+150+220 GHz) extracts clusters
more effectively than one with a high frequency channel (e.g, 150+220+300 GHz).
