Streaming data can arise from a variety of contexts. Important use cases are continuous sensor measurements such as temperature, light or radiation values. In the process, streaming data may also contain data errors that should be cleaned before further use. Many studies from science and practice focus on data cleaning in a static context. However, in terms of data cleaning, streaming data has particularities that distinguish it from static data. In this paper, we have therefore undertaken an intensive exploration of data cleaning of data streams. We provide a detailed analysis of the applicability of data cleaning to data streams. Our theoretical considerations are evaluated in comprehensive experiments. Using a prototype framework, we show that cleaning is not consistent when working with data streams. An additional contribution is the investigation of requirements for streaming technologies in context of data cleaning.