The observed structure of protein interaction networks is corrupted by many false positive/negative links. This observational incompleteness is abstracted as random link removal and a specific, experimentally motivated (spoke) link rearrangement. Their impact on the structural properties of gene-duplication-and-mutation network models is studied. For the degree distribution a curve collapse is found, showing no sensitive dependence on the link removal/rearrangement strengths and disallowing a quantitative extraction of model parameters. The spoke link rearrangement process moves other structural observables, like degree correlations, cluster coefficient and motif frequencies, closer to their counterparts extracted from the yeast data. This underlines the importance to take a precise modeling of the observational incompleteness into account when network structure models are to be quantitatively compared to data.