  We present a velocity dispersion-based mass calibration of the South Pole
Telescope Sunyaev-Zel'dovich effect survey (SPT-SZ) galaxy cluster sample.
Using a homogeneously selected sample of 100 cluster candidates from 720 deg2
of the survey along with 63 velocity dispersion ($\sigma_v$) and 16 X-ray Yx
measurements of sample clusters, we simultaneously calibrate the
mass-observable relation and constrain cosmological parameters. The
calibrations using $\sigma_v$ and Yx are consistent at the $0.6\sigma$ level,
with the $\sigma_v$ calibration preferring ~16% higher masses. We use the full
cluster dataset to measure $\sigma_8(\Omega_ m/0.27)^{0.3}=0.809\pm0.036$. The
SPT cluster abundance is lower than preferred by either the WMAP9 or
Planck+WMAP9 polarization (WP) data, but assuming the sum of the neutrino
masses is $\sum m_\nu=0.06$ eV, we find the datasets to be consistent at the
1.0$\sigma$ level for WMAP9 and 1.5$\sigma$ for Planck+WP. Allowing for larger
$\sum m_\nu$ further reconciles the results. When we combine the cluster and
Planck+WP datasets with BAO and SNIa, the preferred cluster masses are
$1.9\sigma$ higher than the Yx calibration and $0.8\sigma$ higher than the
$\sigma_v$ calibration. Given the scale of these shifts (~44% and ~23% in mass,
respectively), we execute a goodness of fit test; it reveals no tension,
indicating that the best-fit model provides an adequate description of the
data. Using the multi-probe dataset, we measure $\Omega_ m=0.299\pm0.009$ and
$\sigma_8=0.829\pm0.011$. Within a $\nu$CDM model we find $\sum m_\nu =
0.148\pm0.081$ eV. We present a consistency test of the cosmic growth rate.
Allowing both the growth index $\gamma$ and the dark energy equation of state
parameter $w$ to vary, we find $\gamma=0.73\pm0.28$ and $w=-1.007\pm0.065$,
demonstrating that the expansion and the growth histories are consistent with a
LCDM model ($\gamma=0.55; \,w=-1$).
