Help for IntersectSelf says self-intersections are marked with points. The output is a line or curve, not a point, if the self-intersection is a line or curve. Help should be updated so users are not mislead into looking only for points as output from IntersectSelf.
Please see my latest post here. In V7 _IntersectSelf returns a point as wanted and expected on the same curve. I strongly feel this is a V8 regression with the potential for harm.