\( \newcommand{\fnorms}[1]{{\lVert#1\rVert}^2_F} \newcommand{\pr}{\mathrm{P}} \newcommand{\card}[1]{\lvert#1\rvert} \newcommand{\RR}{\mathcal{R}} \) The proof of one the main results of the paper "Dispersion of mass and the complexity of randomized geometric algorithms" has a mistake that does not appear easy to fix. The precise mistake is in the proof of Lemma 7. Specifically, page 1052, line 7 (the equation that provides an upper bound on \(\operatorname{vol} B\)). Where the formula in the paper has the determinant of matrix \(\hat R \), a correct formula would have the determinant of the matrix of normal vectors to the bands defining the parallelepipeds. This invalidates the rest of the argument. Lemma 7 is used in the proof of Theorem 2 (the lower bound for volume approximation), so the mistake invalidates the proof of Theorem 2.