Self-intersecting or overlapping polylines can cause problems if your organization uses geodatabase replication functionality. Prior to creating Replicas it is important to resolve closed polylines, but how do you find them?
ESRI have included a tool in the Data Reviewer extension that does just that (amongst other things). The tool allows the user to check for closed or unclosed polylines or paths, and the instructions can be run on an entire feature class, a subtype, or a set of features selected using a SQL query. The user can also apply a severity rating to the results to indicate the importance the results for quality assurance and control purposes.
Instructions on using the Data Reviewer tool can be found here – this tool is available to those with an ESRI ELA however a trial version is also available.