A new class of Preisach operators based on play operators with an inverse in a closed form and allowing for saturation has recently been proposed. Its existence criteria and identification procedure were considered in earlier articles. The present paper analyses the identification procedure with respect to the sensitivity to underlying functions (i.e. intrinsic behaviour of the hysteretic system), to spline approximation, and to the least square error estimation procedure. The analysis shows that model errors are significantly influenced by large derivatives of the underlying functions. Spline approximations have generally little effect on model errors. In particular, an upper bound of for the relative parameter error due to measurement discrepancies has been derived for the least square error problem. The bound increases, the closer to saturation data are measured.