Essential physical quantities of magnetically confined plasmas are derived on a routine basis from bolometric reconstructions. In the last few years at the Joint European Torus (JET), the Maximum Likelihood method has demonstrated the capability of providing reliable reconstructions for this class of ill-posed problems. The article is focused on quantifying the effects of important sources of errors, usually underestimated, that can influence both the reconstructions and the derived quantities. A complete set of phantoms has been used to test the robustness of the technique. The main sources of uncertainties investigated in this contribution are random noise, presence of outliers in the measurements, uncertainty of the position of the magnetic topology, and missing measurements from damaged or unreliable bolometers. The study provides a comprehensive quantification of the uncertainties to associate with most typical emissivities encountered in practice and constitutes a good basis for a more accurate evaluation of the power balances on the JET.