Problems

Systematic uncertainties? Most of us are comfortable with encoding this in a pdf for the uncertain background, efficiency, etc. Trivial to include even hugely complicated systematic uncertainties in widening of pdf's (generalize H+C).
Discrete events: Unavoidable imperfect coverage in any method.
- Unavoidable conservatism/overcoverage to avoid undercoverage (false exclusion rate lower than specified).
Debates about what the ensemble is.
- Ex: 77 events in Tevatron top mass.
- Higgs mass uncertainty at LEP wouldn't have been easier.

Systematic uncertainties? Most of us are comfortable with encoding this in a pdf for the uncertain background, efficiency, etc. Trivial to include even hugely complicated systematic uncertainties in widening of pdf's (generalize H+C).