Mike said:
I have a Japanese Black Pine in a very large training pot. ...
This past growing season, I noticed some white stuff at the base of
many needles and on some of the shoots. It almost looks like bird
dung,
but I know it isn't. Can anyone venture a guess at what it is and how
to treat it?

I say: Sounds like a pine adelgid: google them and look at the
pictures. They are woolly aphidlike insects. You can treat with a
dormant oil now, which will smother them, or a light summer oil during
the growing season (as directed by label). Otherwise, ask your nearest
Cooperative Extension office for advice on insecticides.