Pump-probe microscopy has recently emerged as an important tool for characterizing the effects of nanoscale chemical and compositional heterogeneity on the optoelectronic properties of material systems. This article describes the development of broadband pump-probe microscopy, which utilizes a high-speed line camera and high repetition rate amplified fiber laser to collect full transient spectra at 30+ kHz and with sub 100 fs temporal resolution. The broadband imaging and spectroscopic capabilities of the technique are demonstrated on individual micron-sized lead halide perovskite domains. Also discussed are several challenges associated with collecting broadband transient spectra from sub-micron sample areas, including the importance of careful design of imaging optics to minimize the effects of spherical and chromatic aberrations, detector considerations, and the importance of spot size effects on absolute signal size.