Both QGIS and QGIS server are being tested via all kind of ways.
From build tests (Travis) and code unit tests to OGC conformance testing.
See Unit testing
See OGC conformance testing for more information and how to run these tests yourself.
Recent tests output can be found here: http://test.qgis.org/ogc_cite. For latest WMS 1.3.0 test see http://test.qgis.org/ogc_cite/wms_130/latest/report.html and for WFS 1.1.0 see http://test.qgis.org/ogc_cite/wfs_110/latest/report.html.