  We present an improved analysis of the final dataset from the QUaD
experiment. Using an improved technique to remove ground contamination, we
double the effective sky area and hence increase the precision of our CMB power
spectrum measurements by ~30% versus that previously reported. In addition, we
have improved our modeling of the instrument beams and have reduced our
absolute calibration uncertainty from 5% to 3.5% in temperature. The robustness
of our results is confirmed through extensive jackknife tests and by way of the
agreement we find between our two fully independent analysis pipelines. For the
standard 6-parameter LCDM model, the addition of QUaD data marginally improves
the constraints on a number of cosmological parameters over those obtained from
the WMAP experiment alone. The impact of QUaD data is significantly greater for
a model extended to include either a running in the scalar spectral index, or a
possible tensor component, or both. Adding both the QUaD data and the results
from the ACBAR experiment, the uncertainty in the spectral index running is
reduced by ~25% compared to WMAP alone, while the upper limit on the
tensor-to-scalar ratio is reduced from r < 0.48 to r < 0.33 (95% c.l). This is
the strongest limit on tensors to date from the CMB alone. We also use our
polarization measurements to place constraints on parity violating interactions
to the surface of last scattering, constraining the energy scale of Lorentz
violating interactions to < 1.5 x 10^{-43} GeV (68% c.l.). Finally, we place a
robust upper limit on the strength of the lensing B-mode signal. Assuming a
single flat band power between l = 200 and l = 2000, we constrain the amplitude
of B-modes to be < 0.57 micro-K^2 (95% c.l.).
