Supernova (SN) measurements have become a key ingredient in current determinations of cosmological parameters. These sources can however be used as standard candles only after correcting their apparent brightness for a number of effects. In this paper, we discuss some limitations imposed by the formalism currently used for such corrections and investigate the impact on cosmological constraints. We show that colour corrections are, in general, expected to be biased. In addition, colour excesses which do not add a significant scatter to the observed SN brightnesses affect the value of cosmological parameters but leave the slope of the colour–luminosity relation unchanged. We quantify these biases in the context of the redshift-dependent dust extinction suggested by the recent detection of intergalactic dust by Ménard et al. Using a range of models for the opacity of the Universe as a function of redshift, we find that colour–magnitude–stretch scaling relations are virtually insensitive to the presence of cosmic dust while cosmological parameters such as ΩM and w are biased at the level of a few per cent, i.e. offsets comparable to the current statistical errors. Future surveys will be able to limit the impact of intergalactic extinction by observing at longer wavelengths. In addition, such data sets will provide direct detections of intergalactic dust by cross-correlating SN colours and the density of foreground galaxies, which can be used as a consistency check on the cosmic dust extinction correction. Alternatively, such biases could be avoided by correcting the colours of SNe on an object-by-object basis with accurate photometry.