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>       The solution is (boringly) more data.  More data & more data.

Sort of.

There have been many, many studies over the past year - primarily published
in Systematic Biology - addressing this very issue.  In nearly all cases,
when it comes to a question of whether characters or taxa should be added,
taxa turn out to be more significant.  And in particular, it's taxa close
to the root that prove critical - an important point in the classic
Gauthier et al. 1988 paper that's often overlooked, but something we see
demonstrated - whether we're using morphology or molecules - in both
empirical and simulation studies.

This does not mean that small data sets will be robust to character
sampling.  I've seen some seriously biased data sets published.  But
"adding more data" won't necessarily be a panacea - we have to be aware of
what kinds of data are likely to prove pivotal.