Is there a limit to the number of genes carried by an organism? Two reasons have been. First, as most mutations are deleterious, for a given per locus mutation rate there must exist an upper limit to the number of genes that is consistent with individual survival. Second, the imprecision of the mechanisms governing gene expression might also restrict genomic complexity. As gene expression errors are probably much more common than mutations, it is the latter that are more likely to impose a limit. However, these errors are not heritable and therefore cannot accumulate in populations. Which of the two sorts of effect are more likely to impose a limit? We address this issue in two ways. First, we ask about the load imposed by each sort of error. We show that the harmful effect of non-heritable failures is higher than that of heritable mutations, if (p) x (delta) > mu, where p is the rate of non-heritable failures, delta measures the harmful effect of these failures and mu is the rate of heritable mutations. Therefore, although the rate of non-heritable errors might be very high, this does not demonstrate that they are more important than mutations as their impact must be discounted by the strength of their effects. Further, we note that both theory and evidence suggest that the most common errors are of the least importance. Second, we discuss the population genetics of a new gene duplication. Previous attempts to make a connection between error rates and limits on gene number are based on group selection arguments. These fail to show a direct limitation on the spread of gene duplications. We note that empirical evidence indicates that duplication per se tends to result in expression errors that may be heritable. We therefore argue that a hybrid model, one evoking heritable expression errors, is likely to be the most realistic.