One effect of anhedral that hasn't been mentioned is that it provides increased stability at high angles of attack. If you look at most if not all modern airliners you will notice that the horizontal stabs appear to have dihedral but with up elevator they are in effect a inverted wing and actually have anhedral. In the nose high attitude for landing or take off some of the effectiveness of the vertical stab is lost due to dirty air from the fuselage so the anhedral tends to add stabilty to the tail. Also a wing with anhedral should have more stability at high angles of attack.
Regarding effective dihedral, some airplanes with high dihedral angles, such as the North American Navion, which despite having a whopping 7 degrees loses it's effective dihedral when the flaps are put down. It then has near neutral stability and will not return to level flight by itself particularly when sideslipped. The fix for this was to add interconnect cables between the ailerons and rudder. This allowed the wing to pick up by simply moving the rudder.