Using an experiment with thin paper layers and computer simulation, we demonstrate the principal limitations of standard Time Domain Spectroscopy (TDS) based on using a broadband THz pulse for the detection and identification of a substance placed inside a disordered structure. We demonstrate the spectrum broadening of both transmitted and reflected pulses due to the cascade mechanism of the high energy level excitation considering, for example, a three-energy level medium. The pulse spectrum in the range of high frequencies remains undisturbed in the presence of a disordered structure. To avoid false absorption frequencies detection, we apply the spectral dynamics analysis method (SDA-method) together with certain integral correlation criteria (ICC).