  We construct two homology 3-spheres for which the (unperturbed) $SU(2)$
Chern-Simons function is not Morse-Bott. In one case, there is a degenerate
isolated critical point. In the other, a path component of the critical set is
not homeomorphic to a manifold. The examples are $+1$ surgeries on connected
sums of torus knots.
