  Massive stars exhibit spectroscopic and photometric variability over a wide
range of timescales. However the physical mechanisms driving this behaviour
remain poorly understood. Westerlund 1 presents an ideal laboratory for
studying these processes in a rich, coeval population of post-main sequence
stars and we present a pathfinding study aimed at characterising their
variability utilising the large body of data that has accumulated since the
1960s. Spectroscopic variability attributable to both wind asphericity and
photospheric pulsations was present amongst both the hot and cool stellar
populations. Given the limitations imposed by the data, we were unable to
determine the physical origin of the wind structure inferred for the OB
supergiants, although the inhomogineities in the winds of the Wolf Rayets are
likely driven by binary interactions and, conversely, by pulsations in at least
one of the cool hypergiants. Photospheric pulsations were found for stars
ranging from spectral types as early as O9 I through to the mid F Ia+ yellow
hypergiants - with a possible dependence on the luminosity class amongst the OB
stars. The spectroscopically variable red supergiants (M2-5 Ia) are also
potential pulsators but require further observations to confirm this
hypothesis. Determination of the amplitude and periodicity of these pulsations
as a function of temperature, luminosity and evolutionary state holds open the
prospect of identifying the physical mechanisms driving the instabilities that
constrain and define stellar evolution in the upper reaches of the HR diagram,
while the presence of highly luminous yellow hypergiants and red supergiants
within Wd1 place strong constraints on post-main sequence evolutionary
pathways, apparently contradicting current theoretical predictions for >25Msun
stars at solar metallicites. [ABRIDGED]
