In order to study the effect of mutation rate heterogeneity on patterns of DNA polymorphism, we simulated samples of DNA sequences with gamma-distributed nucleotide substitution rates in stationary and expanding populations. We find that recent population expansions and mutation rate heterogeneity have similar effects on several polymorphism indicators, like the shape and the mean of the observed pairwise difference distribution, or the number of segregating sites. The inferred size of population expansion thus appears overestimated if nucleotides have dissimilar substitution rates. Interestingly, population expansion and uneven mutation rates have contrasting effects on Tajima's D statistic when acting separately, and the consequence on the associated test of selective neutrality is investigated. The patterns of polymorphism of several human populations analyzed for the mitochondrial control region are examined, mainly showing the difficulty in quantifying the respective contribution of past demographic history and uneven mutation rates from a single sampled evolutionary process. However, substitution rates appear more heterogeneous in the second hypervariable segment of the control region than in the first segment.