Random sequential adsorption (RSA) of polydisperse mixtures of hard and interacting spherical particles was analyzed. Theoretical results were derived by performing numerical MC simulations both for Gaussian and for continuous distributions of particle sizes characterized by standard deviations below 20%. Adsorption kinetics of these mixtures was determined for a broad range of times showing that for tau < 5 the influence of polydispersity was rather minor for both Gauss and continuous particle size distributions. More significant deviations were predicted for the asymptotic adsorption regime close to jamming. In the case of continuous distributions this limiting kinetics could be described by the power law dependence theta(infinity) - theta similar to tau(-1/3) in accordance with the predictions of G. Tarjus and J. Talbot (1991, J. Phys. Math Gen. 24, L913). The jamming concentration theta(infinity) for hard (noninteracting) particles was found to increase proportionally to <(sigma)over bar>. It was also shown that the polydispersity of particle mixtures can exert an effect on the structure of the adsorption layer (characterized in terms of the pair correlation function). The broadening of this function was confirmed experimentally by using colloid suspensions of spherical particles (polystyrene latex) characterized by <(sigma)over bar> = 6-10%.