I think Abdullah Anter has correctly identified what is going on. If I can elaborate, what you are seeing is due to the extremely zoomed-in view causing visual "misrepresentation" of linework that is actually coincident. The coordinate system used was not mentioned, but at this level of zoom, the measurement is probably well below the unit of accuracy used in that coordinate system. So while visually it looks like it is off, it is actually coincident.
Check out the Resolution and Tolerance sections in this link:
The properties of a spatial reference—ArcGIS Help | ArcGIS Desktop
To double-check, check your measurement against the Resolution and Tolerance settings for the dataset. This can be done using ArcCatalog.
For example, here's a feature class I have in a File Geodatabase. If, for example, the image you show was from this feature class, I would say it is coincident and not an issue, as the measurement of 0.000131 feet is below the XY Resolution and Tolerance settings.
For further reference, here's a related issue thread I posted a while back, including ESRI Support's explanation for the visual wierdness experienced when zoomed way in:
Strangeness - gaps unintentionally created while editing
So brings up another way to realize that what is being seen is probably not realistic. In ArcGIS, check the map scale. If it is below 1:1, what you are seeing may not be an accurate depiction of the true nature of the data (i.e. it can look ugly but be fine).
Chris Donohue, GISP