On approaching the glass transition, a dense colloid exhibits a dramatic slowdown with minute structural changes. Most microscopy experiments directly follow the motion of individual particles in real space, whereas scattering experiments typically probe the collective dynamics in reciprocal space at variable wavevector q. Multiscale studies of glassy dynamics are experimentally demanding and, thus, seldom performed. By using two-dimensional hard-sphere colloids at various area fractions ϕ, we show here that Differential Dynamic Microscopy (DDM) can be effectively used to measure the collective dynamics of a glassy colloid in a range of q within a single experiment. As ϕ is increased, the single decay of the intermediate scattering functions is progressively replaced by a more complex relaxation that we fit to a sum of two stretched-exponential decays. The slowest process, corresponding to the long-time particle escapes from caging, has a characteristic time τs = 1/(DLq2) with diffusion coefficient DL∼(ϕc-ϕ)2.8, and ϕc ≃ 0.81. The fast process exhibits, instead, a non-Brownian scaling of the characteristic time τf(q) and a relative amplitude a(q) that monotonically increases with q. Despite the non-Brownian nature of τf(q), we succeed in estimating the short-time diffusion coefficient Dcage, whose ϕ-dependence is practically negligible compared to the one of DL. Finally, we extend DDM to measure the q-dependent dynamical susceptibility χ4(q, t), a powerful yet hard-to-access multiscale indicator of dynamical heterogeneities. Our results show that DDM is a convenient tool to study the dynamics of colloidal glasses over a broad range of time and length scales.