Plastic flow instability attracts increasing interest as a self-organization phenomenon showing various dynamical regimes, including deterministic chaos and self-organized criticality. The analysis of the associated nonrandom noise--drastic jumps of the mechanical stress--however, confronts the variation of the noise average parameters due to the evolution of the dislocation microstructure. The present paper examines some limitations of the multifractal approach to the study of the evolving noise. The applicability of the multifractal analysis to practical situations is proven using the example of discontinuous deformation curves observed under conditions of the Portevin-Le Châtelier effect in an A1Mg alloy, as well as model signals generated by stretching multifractal Cantor sets. It is found that the smooth trends in the stress serration parameters may narrow the range of the scale invariant behavior associated with the multifractal structure, but do not essentially mask it.