Tap keeps dripping even after reseating - broken?
I would say that your excellent picture shows that the seat in this valve is not smooth and planar all the way around. With that said it looks like this valve is definitely in line for replacement. 

As a temporary work around you may want to see if you can find a faucet washer that is made of silicon instead of the normally much harder faucet washer material. It may be able to squeeze down on the imperfect seat and seal off the faucet till you can make the full replacement. Do not wait too long however because the turning under pressure to close the faucet with a silicon washer is likely to degrade and tear up the washer surface.