When a network is inferred from data, two types of errors can occur: false positive and false negative conclusions about the presence of links. We focus on the influence of local network characteristics on the probability α of false positive conclusions, and on the probability β of false negative conclusions, in the case of networks of coupled oscillators. We demonstrate that false conclusion probabilities are influenced by local connectivity measures such as the shortest path length and the detour degree, which can also be estimated from the inferred network when the true underlying network is not known a priori. These measures can then be used for quantification of the confidence level of link conclusions, and for improving the network reconstruction via advanced concepts of link weights thresholding.