This article is concerned with finding trends, maxima, and minima in a curve underlying a scatter plot of observations. When the data exhibit large variation, the detection of such features can be difficult because it is not easy to say which of the seeming features are statistically significant. Additional difficulties emerge when the values of the predictor variable may contain errors and when errors in the response variable cause dependence in their observed values. We propose a Bayesian approach for finding statistically significant features in a scatter plot under such challenging conditions. The method extends in several ways the BSiZer approach earlier introduced by the authors.