The Moran scatterplot is a useful tool for exploring the spatial structure of datasets. The diagram plots spatial lags, that is, averaged spatial neighbourhoods, against their corresponding local attribute values. In this way, differently characterised autocorrelation sectors and structural breaks can be identified. However, the Moran scatterplot does not provide easily identifiable indications of possible spatial weight misspecification and p values. Both are important information when exploring possible spatial structures. In this short paper, so-called Moran seismograms and Moran drop plots are introduced, which complement the Moran scatterplot and visualise both types of information mentioned.