Did you replace the dirty old bearing cages with fresh, new ball bearings? do that if you haven't. Grime is very difficult to clean out of cages and your probably not getting it all. As far as whether or not your headset is any good, look at where the balls contact the race. Is there any pitting or deformity in the race? if yes, then you may want to consider getting a new headset if you plan on having the bike for a long time. You might as well do it now if that IS the case. otherwise your good to go. If your having trouble finding that sweet spot while adjusting, make sure your steerer tube is not bent by holding a straight edge against it. A bent steerer won't allow you to adjust it properly.

If you already did clean everything well AND replace the cages with balls, but you STILL are getting grime in there, its probally coming from inside the frame somehow. I have cleaned out dirty head tubes by blasting it with water, letting it dry, then putting frame saver in.
best of luck
Tim