Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value ¼ c. Here we study the heterogeneous and collective nature of dislocation dynamics within a crystal plasticity model close to c, by considering the first-passage properties of the dislocation dynamics. As the transition is approached in the moving phase, the first-passage time distribution exhibits scaling, and a related peak dynamical susceptibility 4 diverges as 4 ð cÞ , with 1:1. We relate this scaling to an avalanche description of the dynamics. While the static structural correlations are found to be independent of the external stress, we identify a diverging dynamical correlation length y in the direction perpendicular to the dislocation glide motion.