Existing methodology for changepoint localization in an evolving time series of networks generally relies on accurately prescribed vertex correspondence between network realizations at different times. However, such vertex alignments are often misspecified or even unknown. To understand the impact of vertex misalignment on inference for dynamic networks, two illustrative models are constructed for network evolution, each with a similar changepoint. Different techniques are compared for changepoint localization, ranging from the simple network statistic of average degree to the more involved and recently developed procedure of Euclidean mirrors. In one model, vertex misalignment causes comparatively little error, and in the other, it seriously impairs localization, although the Euclidean mirror procedure can nevertheless extract a meaningful signal. It is shown how misalignment between network realizations at different times can effectively weaken their underlying correlation, impeding inference procedures that rely on accurate inference of such correlation. Graph matching and optimal transport is discussed, both of which are potential mechanisms for mitigating errors from misalignment, but which may also fail to improve inference under certain models. Simulations are presented that illustrate these varying effects on approaches to localization.