We point out two errors in the paper ``The integer cohomology algebra of toric arrangements'', Adv. Math., Vol. 313, pp. 746-802, 2017. The main error concerns Theorem 4.2.17. In that theorem's proof, Diagram (8) does not commute in general but only under some restrictive hypotheses on the arrangement $\mathcal{A}$. This invalidates the description for the ring structure of $H^*(M(\mathcal{A});\mathbb{Z})$ given in Theorems A and B. We refer to alternative descriptions of the cohomology ring $H^*(M(\mathcal{A});\mathbb{Z})$. The second error concerns Theorem 7.2.1. The claim does hold, but the proof is incorrect. We refer to a counterexample for the argument given in the proof and we provide references for a correct proof.