I would export your polygons to geodatabase first and have the polygon as a backup.. Once you export it to geodatabase then add the topology and that should help you find the overlaps....
To learn about it go here...ArcGIS Help 10.1
You could use the Integrate tool. You specify an input and a distance and it will move all polygons together if they are within the tolerance.
This tool may change the outline of your polygons significantly if you set the tolerance too high.
Here is the link to the tool.