Stream processing is designed to query unbounded and timely-ordered data flows in real time while guaranteeing low latency and high throughput. Despite its roots in the database community, the most recent research on data stream management has focused on performance and neglected the role of data quality. Moreover, quality management techniques are not always feasible in streaming since the data should “keep moving.” Nevertheless, data quality issues, e.g., timeliness and completeness, become progressively more important as stream processing is applied beyond the context of analytics. For this reason, we advocate for an approach that not only allows data quality intervention as done before but also allows tracking the consistency of the records across streaming queries through provenance annotations. These annotations are associated with the input and propagated to the query results, on which a degree of inconsistency is calculated.