My umbrella tree leaves have developed slash-like marks
almost as if someone cut them with an exacto knife. The slashed part
hangs on by a thread, turns black and then falls off. The cuts
(chews?) can be found in old and new leaves. Is there some pest that
does this sort of damage?

Where in general do you live? By "Umbrella Tree" do you mean Sheffaleria
Arbacola?

I live in Portland, Oregon. The plant is in a medium-light room which
is consistently in the mid 70s temperature-wise. If it would help, I
could send you a picture of an affected leaf.
S.