You could use the **Intersect** function (*Vector* > *Geoprocessing Tools* > *Intersect*) to provide you with another line layer with duplicates. You can then give your 2 layers different colours (eg. make the original layer to be thicker and darker; the intersect layer to be thinner and lighter). 

If you want to see the duplicates in a single line layer then you can use the **Merge shapefiles to one** function (*Vector* > *Data Management Tools* > *Merge shapefiles to one*). Before you do this, make sure you add an additional attribute to each layer. You can then use the *Rule-based* style filtering in the merged layer to differentiate between the original layer and the merged layer.

Hope this helps.