As risk analysts learn and use more advanced statistical methods for characterizing uncertainty in their assessments, care must be taken to avoid systematic errors in model specification and subsequent inference. We argue that misspecifcation of the likelihood function in Bayesian analysis, due to underestimated errors, failure to account for correlations in model-data errors, and failure to consider omitted confounding variables, is a particularly pervasive and difficult problem with potentially serious consequences. An illustrative example with an idealized exposure-risk model is used to demonstrate how such errors can lead to false precision - posterior estimates that appear precise but are in fact inaccurate. Initial guidance is suggested for considering the sensitivity of model results to these types of errors.