Discontinuities in the Born-Oppenheimer (infinite nuclear masses) limit of an artificial molecular system, absent for finite masses, have led MM et al. (2014) to a questioning of Berry phases in some molecular systems. We show here by a rigorous following of the analysis of Longuet-Higgins et al. (1958), that (a) the same phenomena of discontinuities occurs in typical degenerate molecular systems with regular Berry-phase effects, (b) they arise from the non-unique definition of the key quantity, electronic 'vector field', and (c) they can be removed by a different choice of normalization. (c) 2015 Elsevier B.V. All rights reserved.