I have two layers in QGIS, one the coordinate system of WGS84 and another uses GRS80. The two layers overlap, which looks good. My question is do I have to reproject them to the same coordinate system or just leave them as they are? Someone told me that reprojection could introduce inaccuracies to the data. So does it matter if I don't reproject? Under what situations is the reprojection needed?
They are reprojected on the fly to your projects coordinate system.
As long as you won't do any geoprocessing with them, there is no need to reproject your layers.