Process analysis is concerned with analyzing recorded process executions to validate, monitor, or improve the underlying processes according to business goals. In this context, the paradigm of object-centric event data (OCED) has recently emerged, which relates activity executions to multiple objects instead of a single, pre-determined case. Since OCED can integrate various process perspectives simultaneously, it represents real-life activities more accurately than traditional event logs. Being the input of Object-Centric Process Mining (OCPM), the quality of the data recorded in OCED logs directly influences the results of the process analysis. To ensure reliable outcomes, it is imperative to assess potential quality problems manifesting in the data. While frameworks for such an assessment are available for classic event data, equivalent approaches for assessing quality issues in OCED do not yet exist. This paper provides an analysis and classification of data quality issues in OCED, and compares them to the issues in traditional event data. Thus, this study is a first step in the systematic assessment and management of data quality in OCED.