RivEX requires your river network to be topologically correct for it to successfully process. Various errors can occur when a network is created and/or updated.

RivEX provides a set of quality controls which you can run on your network. The output of a quality control is a table in a File GeoDatabase identifying the polylines which failed the quality control. It is then up to you, the user, to correct your data.
More advice is given in the manual about dealing with these errors:

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Polyline attributes

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Null (zero) length polylines

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Multi-part polylines

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Self-intersecting polylines

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Closed (looped) polylines

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Small polylines composed of two vertices

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Disconnected polylines

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Double digitised polylines

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Intersecting polylines

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Overlapping polylines

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Duplicate geometry

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Sources within network

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Network cycles

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Polyline spikes

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Stacked vertices

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Identify and remove collinear vertices from a polyline

RivEX also provides a tool for automatically removing self-intersections

Quality controlling your river network