  During the last decade, M87's jet has been the site of an extraordinary
variability event, with one knot (HST-1) increasing by over a factor 100 in
brightness. Variability was also seen on timescales of months in the nuclear
flux. Here we discuss the optical-UV polarization and spectral variability of
these components, which show vastly different behavior. HST-1 shows a highly
significant correlation between flux and polarization, with P increasing from
$\sim 20%$ at minimum to >40% at maximum, while the orientation of its electric
vector stayed constant. HST-1's optical-UV spectrum is very hard
($\alpha_{UV-O}\sim0.5$, $F_\nu\propto\nu^{-\alpha}$), and displays "hard lags"
during epochs 2004.9-2005.5, including the peak of the flare, with soft lags at
later epochs. We interpret the behavior of HST-1 as enhanced particle
acceleration in a shock, with cooling from both particle aging and the
relaxation of the compression. We set 2$\sigma$ upper limits of $0.5 \delta$
parsecs and 1.02$c$ on the size and advance speed of the flaring region. The
slight deviation of the electric vector orientation from the jet PA, makes it
likely that on smaller scales the flaring region has either a double or twisted
structure. By contrast, the nucleus displays much more rapid variability, with
a highly variable electric vector orientation and 'looping' in the $(I,P)$
plane. The nucleus has a much steeper spectrum ($\alpha_{UV-O} \sim 1.5$) but
does not show UV-optical spectral variability. Its behavior can be interpreted
as either a helical distortion to a steady jet or a shock propagating through a
helical jet.
