Twitter and related social media feeds have become valuable data sources to many fields of research. Numerous researchers have thereby used social media posts for spatial analysis, since many of them contain explicit geographic locations. However, despite its widespread use within applied research, a thorough understanding of the underlying spatial characteristics of these data is still lacking. In this paper, we investigate how topological outliers influence the outcomes of spatial analyses of social media data. These outliers appear when different users contribute heterogeneous information about different phenomena simultaneously from similar locations. As a consequence, various messages representing different spatial phenomena are captured closely to each other, and are at risk to be falsely related in a spatial analysis. Our results reveal indications for corresponding spurious effects when analyzing Twitter data. Further, we show how the outliers distort the range of outcomes of spatial analysis methods. This has significant influence on the power of spatial inferential techniques, and, more generally, on the validity and interpretability of spatial analysis results. We further investigate how the issues caused by topological outliers are composed in detail. We unveil that multiple disturbing effects are acting simultaneously and that these are related to the geographic scales of the involved overlapping patterns. Our results show that at some scale configurations, the disturbances added through overlap are more severe than at others. Further, their behavior turns into a volatile and almost chaotic fluctuation when the scales of the involved patterns become too different. Overall, our results highlight the critical importance of thoroughly considering the specific characteristics of social media data when analyzing them spatially.