  We explore extensions to the $\Lambda$CDM cosmology using measurements of the
cosmic microwave background (CMB) from the recent SPT-SZ survey, along with
data from WMAP7 and measurements of $H_0$ and BAO. We check for consistency
within $\Lambda$CDM between these datasets, and find some tension. The CMB
alone gives weak support to physics beyond $\Lambda$CDM, due to a slight trend
relative to $\Lambda$CDM of decreasing power towards smaller angular scales.
While it may be due to statistical fluctuation, this trend could also be
explained by several extensions. We consider running index (nrun), as well as
two extensions that modify the damping tail power (the primordial helium
abundance $Y_p$ and the effective number of neutrino species $N_{\rm eff}$) and
one that modifies the large-scale power due to the ISW effect (the sum of
neutrino masses $\sum m_\nu$). These extensions have similar observational
consequences and are partially degenerate when considered simultaneously. Of
the 6 one-parameter extensions considered, we find CMB to have the largest
preference for nrun with -0.046<nrun<-0.003 at 95% confidence, which
strengthens to a 2.7$\sigma$ indication of nrun<0 from CMB+BAO+$H_0$.
Detectable non-zero nrun is difficult to explain in the context of
single-field, slow-roll inflation models. We find $N_{\rm eff}=3.62\pm0.48$ for
the CMB, which tightens to $N_{\rm eff}=3.71\pm0.35$ from CMB+BAO+$H_0$. Larger
values of $N_{\rm eff}$ relieve the mild tension between CMB, BAO and $H_0$.
When the SZ selected galaxy cluster abundances ($\rm{SPT_{CL}}$) data are also
included, we obtain $N_{\rm eff}=3.29\pm0.31$. Allowing for $\sum m_\nu$ gives
a 3$\sigma$ detection of $\sum m_\nu$>0 from CMB+BAO+$H_0$+$\rm{SPT_{CL}}$. The
median value is $(0.32\pm0.11)$ eV, a factor of six above the lower bound set
by neutrino oscillation observations. ... [abridged]
