Hundreds of thousands of rumours emerge every day. Algorithmic models shall therefore support users of social platforms and provide alerts to prevent users from accidentally spreading rumours. However, existing alerting mechanisms are limited to post-hoc classification, and rumours are often detected after the damage has been done. This paper presents exRumourLens, a system that enables tracking and auditing of potential rumours as they emerge. To this end, it identifies local anomalies related to individual entities, as well as global anomalies on the level of subgraphs of a network of entities. exRumourLens provides various views on such local and global anomalies, thereby providing detailed explanations on emerging rumours and supporting their critical exploration.