This is almost certainly due to QGIS. You might want to try to find someone that can do a known good reprojection for you that was made in ArcGIS or something so you can compare it to your QGIS results.
It can be hard to tell relative elevations in an absolute numbers sense from the colorized DEM image since the color bands each take up a couple of meters. To me, it looks like there is roughly a 2 meter difference between the road doing under the tunnel and the road over the tunnel. That is without actually referring to the values in the DEM image itself. We are in the process of adding a elevation lookup mouse over function.