Two facts:
1. Footnotes can be set to restart on each new section.
2. A new section can start on the same page as the
previous section.
You realize, if it was possible to combine (1) and (2),
that Word might produce the same footnote number twice on
a page. In other words, there is a perfectly good reason
why footnotes and continuous section breaks don't work
well together.
A work-around is presented by Suzanne S. Barnhill in the
article found at
http://word.mvps.org/FAQs/Formatting/FtnoteSpanColumns.htm
Suzanne characterizes her workaround as "clumsy". A
different, possibly even more clumsy, workaround is to use
a table instead of newspaper columns, if you ever need to
use both multiple and single column layout on the same
page, which would eliminate the need for a pair of
continuous section breaks.
Stefan Blom