Continuum intensity observations obtained with the Michelson Doppler Imager (MDI) on board the SOHO mission provide long time series of filtergrams that are ideal for studying the evolution of large-scale phenomena in the solar atmosphere and their dependence on solar activity. These filtergrams, however, are not taken in a pure continuum spectral band, but are constructed from a proxy, namely a combination of filtergrams sampling the Ni I 6768 Å line. We studied the sensitivity of this continuum proxy to the shape of the nickel line and to the degradation in the instrumental transmission profiles. We compared continuum intensity measurements near the nickel line with MDI proxy values in three sets of high-resolution spectro-polarimetric data obtained with the Interferometric Bidimensional Spectrometer, and in synthetic data, obtained from multi-dimensional simulations of magneto-convection and one-dimensional atmosphere models. We found that MDI continuum measurements require brightness corrections which depend on magnetic field strength, temperature and, to a smaller extent, plasma velocity. The correction ranges from 2% to 25% in sunspots, and is, on average, less than 2% for other features. The brightness correction also varies with position on the disk, with larger variations obtained for sunspots, and smaller variations obtained for quiet Sun, faculae, and micropores. Correction factors derived from observations agree with those deduced from the numerical simulations when observational effects are taken into account. Finally, we found that the investigated potential uncertainties in the transmission characteristics of MDI filters only slightly affect the brightness correction to proxy measurements.