Is there a setting whereby footnotes that cover more than
one page have some sort of designation (.e.g. "continued on
next page") that shows that fact?
In fact, there is. Two even.
Switch into Normal View and go to View | Footnotes. A footnote pane will
open up at the bottom, with a dropdown menu. Use the dropdown menu and you
will see that you have the option of seeing and editing:
--Footnotes
--Footnote Separator--that little line between notes and text
--Footnote Continuation Separator--a line that goes all the way across the
page when the first note text is text continued from note on the previous
page
--Footnote Continuation Notice--text you can insert to appear at the end of
the previous page informing one that the note is continued on the next.
Blank by default, you can enter your own text.
I've always considered that the FCS (the full line) is enough notice without
using the FCN, myself. There are exactly parallel settings for Endnotes, by
the way.