A critical discussion of the assumption of uncorrelated errors in classical psychometric theory and its applications is provided. It is pointed out that this assumption is essential for a number of fundamental results and underlies the concept of parallel tests, the Spearman-Brown's prophecy and the correction for attenuation formulas as well as the discrepancy between observed and true correlations, and the upper bound property of the reliability index with respect to validity. These relationships are shown not to hold if the errors of considered pairs of tests are correlated. The assumption of lack of error correlation is demonstrated not to be testable using standard covariance structure analysis for pairs of indivisible measures evaluating the same true score with identical error variances.