  In the context of ultracold atoms in multimode optical cavities, the
appearance of a quantum-critical glass phase of atomic spins has been predicted
recently. Due to the long-range nature of the cavity-mediated interactions, but
also the presence of a driving laser and dissipative processes such as cavity
photon loss, the quantum optical realization of glassy physics has no analog in
condensed matter, and could evolve into a "cavity glass microscope" for
frustrated quantum systems out-of-equilibrium. Here we develop the
non-equilibrium theory of the multimode Dicke model with quenched disorder and
Markovian dissipation. Using a unified Keldysh path integral approach, we show
that the defining features of a low temperature glass, representing a critical
phase of matter with algebraically decaying temporal correlation functions, are
seen to be robust against the presence of dissipation due to cavity loss. The
universality class however is modified due to the Markovian bath. The presence
of strong disorder leads to an enhanced equilibration of atomic and photonic
degrees of freedom, including the emergence of a common low-frequency effective
temperature. The imprint of the atomic spin glass physics onto a "photon glass"
makes it possible to detect the glass state by standard experimental techniques
of quantum optics. We provide an unambiguous characterization of the
superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne
detection, and the temporal photon correlation function $g^{(2)}(\tau)$.
