  We present deep 1.2 mm continuum mapping of a 566 arcmin^2 area within the
Lockman Hole North field, previously a target of the Spitzer Wide-area Infrared
Extragalactic (SWIRE) survey and extremely deep 20 cm mapping with the Very
Large Array, which we have obtained using the Max-Planck millimeter bolometer
(MAMBO) array on the IRAM 30 m telescope. After filtering, our full map has an
RMS sensitivity ranging from 0.45 to 1.5 mJy/beam, with an average of 0.75
mJy/beam. Using the pixel flux distribution in a map made from our best data,
we determine the shape, normalization, and approximate flux density cutoff for
1.2 mm number counts well below our nominal sensitivity and confusion limits.
After validating our full dataset through comparison with this map, we
successfully detect 41 1.2 mm sources with S/N > 4.0 and S(1.2 mm)\simeq 2-5
mJy. We use the most significant of these detections to directly determine the
integral number counts down to 1.8 mJy, which are consistent with the results
of the pixel flux distribution analysis. 93% of our 41 individual detections
have 20 cm counterparts, 49% have Spitzer/MIPS 24 micron counterparts, and one
may have a significant Chandra X-ray counterpart. We resolve \simeq 3% of the
cosmic infrared background (CIB) at 1.2 mm into significant detections, and
directly estimate a 0.05 mJy faint-end cutoff for the counts that is consistent
with the full intensity of the 1.2 mm CIB. The median redshift of our 17
detections with spectroscopic or robust photometric redshifts is z(median)=2.3,
and rises to z(median)=2.9 when we include redshifts estimated from the
radio/far-infrared spectral index. By using a nearest neighbor and angular
correlation function analysis, we find evidence that our S/N>4.0 detections are
clustered at the 95% confidence level.
