Understanding the plastic deformation mechanisms of disordered materials is a longstanding and complex problem in condensed matter physics and materials science. In particular, the elementary plastic rearrangement in a disordered material is believed to be the shear transformation zone, a localized cooperative motion of a handful of constituents. Although observed in mesoscale systems, the shear transformation zone has never been identified in an experiment at the nanoscale. In the present work, atomic force microscopy is used to probe the mechanical response of thin films of disordered nanoparticle packings that have been deposited by spin-coating and layer-by-layer deposition. Results demonstrate that these materials possess strong heterogeneity in their mechanical properties, which has also been observed in other materials including metallic glass. Topography imaging provides nanometer-level resolution, which allows rearrangements to be observed directly. These are the first rearrangements observed in a three-dimensional disordered material at the nanoscale. By changing the relative humidity in the atomic force microscope chamber, the size of the condensed capillary is controlled. It is found that increasing the humidity causes the nanoparticle film to transition from a strong, brittle state under ambient conditions to a more ductile state at relative humidity above 90%. At saturation, a nearly viscous state is observed. Disordered nanoparticle packings exhibit rearrangement events featuring avalanche scaling, which has previously been witnessed in numerous other materials including metallic glass and rocks. This is the first time that avalanche scaling has been observed in nanoscale granular materials. The number of rearrangement events is found to increase at high ambient humidity, but the shape of the distribution remains consistent regardless of the environmental conditions. This suggests that avalanche scaling is independent of the strength of particle interactions. The results presented in this work have implications how nanoparticle thin films might be toughened in commercial applications where they may be subjected to external stress. In addition, the close match in behavior between these nanoparticle packings and other disordered systems suggests that findings related to the present materials can also be applied to other disordered materials, including atomic glasses that cannot be probed at the constituent length scale.