The problem of observation error in assessing the dynamics of populations over time has received increasing attention of late. Of particular interest has been a density-independent dynamic model, which allows a trend and is commonly employed in population viability analysis (PVA). Most of the recent work in this area has focused on assessing the impact of the observation error and on finding corrected estimators, primarily under normal models with the observation errors assumed to have a constant variance. This paper provides a comprehensive overview of statistical methods for this problem and evaluates them through simulations. This includes the development and assessment of simple and practical ways to obtain standard errors and confidence intervals for the basic parameters in the model and functions of them, such as the intrinsic rate of increase or the probability of eventual extinction. We allow for unequally spaced data and possibly changing observation error variances, and we also discuss how to employ standard errors that often accompany the estimated abundances. Both likelihood techniques under normality and methods allowing non-normal observation errors are discussed, and we describe how the various likelihood-based techniques can be implement using standard mixed-model software, such as PROC MIXED in SAS. The projection technique we use to handle functions of the basic parameters is also valuable when there is no observation error. The methods are motivated and illustrated using data for grizzly bears, Whooping Cranes, California Condors, and Puerto Rican Parrots. We present a simulation experiment to evaluate the performance of the some of the methods.