Scientific network analysis takes at input large amounts of bibliographical data that are often incomplete. This leads to the introduction of different measurement errors in the scientific networks, which, in turn, influence the results of scientific networks analyses. Different authors have been studying the effects of measurement error on the results of network analysis, but these studies mostly rely on data gathered by survey questionnaires or on the study of incomplete data that are shown as random processes and emerge in unweighted undirected networks. This article aims at overcoming the limitations of these studies in three directions. First, we introduce measurement errors to network data following three most frequently present and well-known problems often present in bibliographic data: multiple authorship, homographs, and synonyms. Second, we apply missing data mechanisms to the identified incomplete data sources in order to link the latter with the probability of their occurrence. Third, we apply the incomplete data sources to different types of scientific networks and study the effects of measurement error in both, the weighted directed (i.e., citation) network and the weighted undirected (i.e., co-authorship) network. The results show that the most destructive incomplete data source is the problem of synonyms; it influences the accuracy and the robustness of the network structural measures the most. On the other hand, the multiple-authorship problem does not influence the results of network analysis at all.