We report the results of a synoptic study of the photometric and spectroscopic variability of the classical T Tauri star AA Tau on timescales ranging from a few hours to several weeks. Emission lines show both infall and outflow signatures and are well reproduced by magnetospheric accretion models with moderate mass accretion rates and high inclinations. The veiling shows variations that indicate the presence of 2 rotationally modulated hot spots corresponding to the two magnetosphere poles. It correlates well with the HeI line flux, with B-V and the V excess flux. We have indications of a time delay between the main emission lines and veiling, the lines formed farther away preceding the veiling changes. The time delay we measure is consistent with accreted material propagating downwards the accretion columns at free fall velocity from a distance of about 8 Rstar. We also report periodic radial velocity variations of the photospheric spectrum which might point to the existence of a 0.02 Msun object orbiting the star at a distance of 0.08 AU. During a few days, the variability of the system was strongly reduced and the line fluxes and veiling severely depressed. We argue that this episode of quiescence corresponds to the temporary disruption of the magnetic configuration at the disk inner edge. The radial velocity variations of inflow and outflow diagnostics in the Halpha profile yield further evidence for large scale variations of the magnetic configuration on a timescale of a month. These results may provide the first clear evidence for large scale instabilities developping in T Tauri magnetospheres as the magnetic field lines are twisted by differential rotation between the star and the inner disk.