  In any calculation in perturbative Quantum Chromodynamics (QCD) a choice
needs to be made for the unphysical renormalisation scale, $\mu_R$. The
Brodsky-Lepage-Mackenzie/Principle of Maximum Conformality (BLM/PMC)
scale-setting procedure is one proposed method for selecting this scale. In
this work we identify three ambiguities in the BLM/PMC procedure itself. Their
numerical impact is studied using the example of the total cross-section for
$t\bar{t}$ production through Next-to-Next-to-Leading Order in QCD. One
ambiguity is the arbitrary choice of the value of the highest-order PMC scale.
The numerical impact of this choice on the BLM/PMC prediction for the
cross-section is found to be comparable to the impact of the choice of $\mu_R$
in the conventional scale-setting approach. Another ambiguity relates to the
definitions of the other PMC scales and is similarly found to have a large
impact on the cross-section.
