  We present a catalog of 510 radio-loud active galactic nuclei (AGN, primarily
blazars) and 287 dusty star-forming galaxies (DSFGs) detected by the Atacama
Cosmology Telescope at $>5\sigma$ significance in bands centered on 148 GHz (2
mm), 218 GHz (1.4 mm) and 277 GHz (1.1 mm), from a 480 square degrees strip on
the celestial equator with additional (360 square degrees) shallower fields.
Combining the deepest available 218 GHz wide-field imaging, 277 GHz data, and
multi-band filtering yields the most sensitive wide-field millimeter-wave DSFG
selection to date with rms noise referenced to 218 GHz reaching $<2$ mJy. We
developed techniques to remove Galactic contamination from the extragalactic
catalog, yielding 321 additional Galactic sources. We employ a new flux
debiasing method that handles the heterogeneous sample selection due to
Galactic cuts. We present spectral properties and source counts of the AGN and
DSFGs. The DSFG spectra depart from an optically thin modified blackbody
between 218 GHz and 277 GHz, consistent with optically thick emission or an
additional cold dust component. For bright AGN, the inter-year RMS fractional
deviation in flux density from source variability is $\sim40\%$. We report
8$-$2870 mJy source counts for AGN and 8$-$90 mJy source counts for DSFGs, the
latter probing both the brighter, lensed population and the fainter, unlensed
population. At 277 GHz we report the first source counts measurements at these
flux densities, finding an excess above most model count predictions. Finally,
we select thirty of the brightest DSFGs for multi-frequency study as candidate
high-$z$ lensed systems.
