Femtosecond laser excitation of a Co/Pt bilayer results in the efficient emission of picosecond THz pulses. Two known mechanisms for generating THz emission are spin-polarized currents through a Co/Pt interface, resulting in helicity-independent electric currents in the Pt layer due to the inverse spin-Hall effect and helicity-dependent electric currents at the Co/Pt interface due to the inverse spin-orbit torque effect. Here we explore how roughness, crystal structure and intermixing at the Co/Pt interface affect the efficiency of the THz emission. In particular, we varied the roughness of the interface, in the range of 0.1-0.4 nm, by tuning the deposition pressure conditions during the fabrication of the Co/Pt bilayers. To control the intermixing at the Co/Pt interface a 1-2 nm thick CoxPt1-x alloy spacer layer was introduced with various compositions of Co and Pt. Finally, the crystal structure of Co was varied from face centered cubic to hexagonal close packed. Our study shows that the roughness of the interface is of crucial importance for the efficiency of helicity-dependent THz emission induced by femtosecond laser pulses. However, it is puzzling that intermixing while strongly enhancing the helicity-independent THz emission had no effect on the helicity-dependent THz emission which is suppressed and similar to the smooth interfaces.