  For a property $\cal P$ of simplicial complexes, a simplicial complex
$\Gamma$ is an obstruction to $\cal P$ if $\Gamma$ itself does not satisfy
$\cal P$ but all of its proper restrictions satisfy $\cal P$. In this paper, we
determine all obstructions to shellability of dimension $\le 2$, refining the
previous work by Wachs. As a consequence we obtain that the set of obstructions
to shellability, that to partitionability and that to sequential
Cohen-Macaulayness all coincide for dimensions $\le 2$. We also show that these
three sets of obstructions coincide in the class of flag complexes. These
results show that the three properties, hereditary-shellability,
hereditary-partitionability, and hereditary-sequential Cohen-Macaulayness are
equivalent for these classes.
