Methods developed over the past decade have made it possible to estimate molecular demographic parameters such as effective population size, divergence time, and gene flow with unprecedented accuracy and precision. However, they make simplifying assumptions about certain aspects of the species' histories and the nature of the genetic data, and it is not clear how robust they are to violations of these assumptions. Here, we use simulated data sets to examine the effects of a number of violations of the "Isolation with Migration" (IM) model, including intralocus recombination, population structure, gene flow from an unsampled species, linkage among loci, and divergent selection, on demographic parameter estimates made using the program IMA. We also examine the effect of having data that fit a nucleotide substitution model other than the two relatively simple models available in IMA. We find that IMA estimates are generally quite robust to small to moderate violations of the IM model assumptions, comparable with what is often encountered in real-world scenarios. In particular, population structure within species, a condition encountered to some degree in virtually all species, has little effect on parameter estimates even for fairly high levels of structure. Likewise, most parameter estimates are robust to significant levels of recombination when data sets are pared down to apparently nonrecombining blocks, although substantial bias is introduced to several estimates when the entire data set with recombination is included. In contrast, a poor fit to the nucleotide substitution model can result in an increased error rate, in some cases due to a predictable bias and in other cases due to an increase in variance in parameter estimates among data sets simulated under the same conditions.