We consider two aspects of scattering in strong plane-wave backgrounds. First, we show that the infrared divergences in elastic scattering depend on the structure of the background, but can be removed using the usual Bloch-Nordsieck approach. Second, we analyze the infinite series of shifted-mass-shell poles in the particle (Volkov) propagator using lightfront quantization. The complete series of poles is shown to describe a single, on-shell, propagating particle.