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We present a catalog of 68 galaxy clusters, of which 19 are new discoveries, detected via the Sunyaev-Zel'dovich effect (SZ) at 148 GHz in the Atacama Cosmology Telescope (ACT) survey on the celestial equator. With this addition, the ACT collaboration has reported a total of 91 optically confirmed, SZ detected clusters. The 504 square degree survey region includes 270 square degrees of overlap with SDSS Stripe 82, permitting the confirmation of SZ cluster candidates in deep archival optical data. The subsample of 48 clusters within Stripe 82 is estimated to be 90% complete for <em>M</em>500<em>c</em> > 4.5 × 1014M⊙and redshifts 0.15 < <em>z</em> < 0.8. While a full suite of matched filters is used to detect the clusters, the sample is studied further through a ''Profile Based Amplitude Analysis'' using a statistic derived from a single filter at a fixed θ500 = 59 angular scale. This new approach incorporates the cluster redshift along with prior information on the cluster pressure profile to fix the relationship between the cluster characteristic size (<em>R</em>500) and the integrated Compton parameter (<em>Y</em>500). We adopt a one-parameter family of ''Universal Pressure Profiles'' (UPP) with associated scaling laws, derived from X-ray measurements of nearby clusters, as a baseline model. Three additional models of cluster physics are used to investigate a range of scaling relations beyond the UPP prescription. Assuming a concordance cosmology, the UPP scalings are found to be nearly identical to an adiabatic model, while a model incorporating non-thermal pressure better matches dynamical mass measurements and masses from the South Pole Telescope. A high signal to noise ratio subsample of 15 ACT clusters with complete optical follow-up is used to obtain cosmological constraints. We demonstrate, using fixed scaling relations, how the constraints depend on the assumed gas model if only SZ measurements are used, and show that constraints from SZ data are limited by uncertainty in the scaling relation parameters rather than sample size or measurement uncertainty. We next add in seven clusters from the ACT Southern survey, including their dynamical mass measurements, which are based on galaxy velocity dispersions and thus are independent of the gas physics. In combination with WMAP7 these data simultaneously constrain the scaling relation and cosmological parameters, yielding 68% confidence ranges described by σ8 = 0.829 ± 0.024 and Ω<em>m</em> = 0.292 ± 0.025.. We consider these results in the context of constraints from CMB and other cluster studies. The constraints arise mainly due to the inclusion of the dynamical mass information and do not require strong priors on the SZ scaling relation parameters. The results include marginalization over a 15% bias in dynamical masses relative to the true halo mass. In an extension to ΛCDM that incorporates non-zero neutrino mass density, we combine our data with WMAP7, Baryon Acoustic Oscillation data, and Hubble constant measurements to constrain the sum of the neutrino mass species to be∑ν<em>m</em>ν < 0.29 eV (95% confidence limit).