  We show that there exists a non-trivial simplified broken Lefschetz fibration
which has infinitely many homotopy classes of sections. We also construct a
non-trivial simplified broken Lefschetz fibration which has a section with
non-negative square. It is known that no Lefschetz fibration satisfies either
of the above conditions. Smith proved that every Lefschetz fibration has only
finitely many homotopy classes of sections, and Smith and Stipsicz
independently proved that a Lefschetz fibration is trivial if it has a section
with non-negative square. So our results indicate that there are no
generalizations of the above results to broken Lefschetz fibrations. We also
give a necessary and sufficient condition for the total space of a simplified
broken Lefschetz fibration with a section admitting a spin structure, which is
a generalization of Stipsicz's result on Lefschetz fibrations.
