We present a setup for time-resolved spectroscopic ellipsometry in a pump-probe scheme using femtosecond laser pulses. As a probe, the system deploys supercontinuum white light pulses that are delayed with respect to single-wavelength pump pulses. A polarizer-sample-compensator-analyzer configuration allows ellipsometric measurements by scanning the compensator azimuthal angle. The transient ellipsometric parameters are obtained from a series of reflectance-difference spectra that are measured for various pump-probe delays and polarization (compensator) settings. The setup is capable of performing time-resolved spectroscopic ellipsometry from the near-infrared through the visible to the near-ultraviolet spectral range at 1.3 eV-3.6 eV. The temporal resolution is on the order of 100 fs within a delay range of more than 5 ns. We analyze and discuss critical aspects such as fluctuations of the probe pulses and imperfections of the polarization optics and present strategies deployed for circumventing related issues.