Context. The Sunyaev-Zel’dovich (SZ) effect is a powerful tool for studying clusters of galaxies and cosmology. Large mm-wave telescopes are now routinely detecting and mapping the SZ effect in a number of clusters, measure their comptonisation parameter and use them as probes of the large-scale structure and evolution of the universe. Aims. We show that estimates of the physical parameters of clusters (optical depth, plasma temperature, peculiar velocity, non-thermal components etc.) obtained from ground-based multi-band SZ photometry can be significantly biased, owing to the reduced frequency coverage, to the degeneracy between the parameters and to the presence of a number of independent components larger than the number of frequencies measured. We demonstrate that low-resolution spectroscopic measurements of the SZ effect that also cover frequencies >270 GHz are effective in removing the degeneracy. Methods. We used accurate simulations of observations with lines-of-sight through clusters of galaxies with different experimental configurations (4-band photometers, 6-band photometer, multi-range differential spectrometer, full coverage spectrometers) and different intracluster plasma stratifications. Results. We find that measurements carried out with ground-based few-band photometers are biased towards high electron temperatures and low optical depths, and require coverage of high frequency and/or independent complementary observations to produce unbiased information; a differential spectrometer that covers 4 bands with a resolution of ~6 GHz eliminates most if not all bias; full-range differential spectrometers are the ultimate resource that allows a full recovery of all parameters.