  Supernova 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 color corrections are, in general, expected to be
biased. In addition, color 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 color-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 Menard et
al. (2009). Using a range of models for the opacity of the Universe as a
function of redshift, we find that color-magnitude-stretch scaling relations
are virtually insensitive to the presence of cosmic dust while cosmological
parameters such as Omega_M and w are biased at the level of a few percent, i.e.
offsets comparable to the current statistical errors.
  Future surveys will be able to limit the impact of intergalactic extinction
by observing at larger wavelengths. In addition such datasets will provide
direct detections of intergalactic dust by cross-correlating SN colors 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 colors of supernovae on an object-by-object basis with
accurate photometry.
