  We study the mechanical stability of a tunable high-finesse microcavity under
ambient conditions and investigate light-induced effects that can both suppress
and excite mechanical fluctuations. As an enabling step, we demonstrate the
ultra-precise electronic stabilization of a microcavity. We then show that
photothermal mirror expansion can provide high-bandwidth feedback and improve
cavity stability by almost two orders of magnitude. At high intracavity power,
we observe self-oscillations of mechanical resonances of the cavity. We explain
the observations by a dynamic photothermal instability, leading to parametric
driving of mechanical motion. For an optimized combination of electronic and
photothermal stabilization, we achieve a feedback bandwidth of $500\,$kHz and a
noise level of $1.1 \times 10^{-13}\,$m rms.
